Method I

Changing the fractions to descending and ordering.

$\frac{3}{4}$ = 0.75

$\frac{5}{8}$ = 0.625

The decimals will then be:

0.75, 0.8, 0.625, 0.65

Arranging the above in descending order will be:

0.8, 0.75, 0.65, 0.625

The descending order will therefore be:

0.8, $\frac{3}{4}$, 0.65, $\frac{5}{8}$

Method II

Changing the decimals to fractions and ordering

The fractions will be:

$\frac{3}{4}$, $\frac{4}{5}$, $\frac{5}{8}$, $\frac{13}{20}$

$\frac{3}{4}$ = $\frac{\mathrm{3\; x\; 10}}{\mathrm{4\; x\; 10}}$ = $\frac{30}{40}$

$\frac{4}{5}$ = $\frac{\mathrm{4\; x\; 8}}{\mathrm{5\; x\; 8}}$ = $\frac{32}{40}$

$\frac{5}{8}$ = $\frac{\mathrm{5\; x\; 5}}{\mathrm{8\; x\; 5}}$ = $\frac{25}{40}$

$\frac{13}{20}$ = $\frac{\mathrm{13\; x\; 2}}{\mathrm{20\; x\; 2}}$ = $\frac{26}{40}$

Now arrange them in descending order based on the magnitude of the numerators.

32 > 30 > 26 > 25

32 is for $\frac{4}{5}$ which was from 0.8

30 is for $\frac{3}{4}$

26 is for $\frac{13}{20}$ which was from 0.65

25 is for $\frac{5}{8}$

The descending order will therefore be:

0.8, $\frac{3}{4}$, 0.65, $\frac{5}{8}$

From 9:45 am to 12 pm is 2 hours 15 minutes

Notes:

1. 9:45 am + 2 hours = 11:45 am
2. From 11:45 am to 12 pm is 15 minutes

From 12 pm to 4:15 pm is 4 hours 15 minutes

Total hours = 2 hours + 4 hours = 6 hours

Total minutes = 15 minutes + 15 minutes = 30 minutes

Time spent = 6 hours 30 minutes

Method I

Using proportionality

The total fraction is 1

Fraction of learners who failed + Fraction of learners who passed = 1

Fraction of learners who failed = 1 - Fraction of learners who passed

Fraction of learners who failed = 1 - $\frac{2}{3}$

Every whole number is being divided by 1 but it is not written.

1 = $\frac{1}{1}$

Fraction of learners who failed = $\frac{1}{1}$ - $\frac{2}{3}$

Fraction of learners who failed = $\frac{\mathrm{1\; x\; 3\; -\; 2\; x\; 1}}{3}$

Fraction of learners who failed = $\frac{\mathrm{3\; -\; 2}}{3}$

Fraction of learners who failed = $\frac{1}{3}$

Number of learners who failed = 69

If $\frac{1}{3}$ = 69

$\frac{2}{3}$ = $\frac{2}{3}$ x 69 ÷ $\frac{1}{3}$

$\frac{2}{3}$ = $\frac{2}{3}$ x 69 x $\frac{3}{1}$ = $\frac{\mathrm{2\; x\; 69\; x\; 3}}{\mathrm{3\; x\; 1}}$ = 2 x 69 = 138

Alternatively,

Treating the fractions as parts:

$\frac{2}{3}$ can be seen as the class being divided into 3 parts

Total parts = 3

Passed parts = 2

Failed parts = 3 - 2 = 1

Now use the proportionality rule

If 1 part = 69

2 pars = $\frac{\mathrm{2\; x\; 69}}{1}$ = 2 x 69 = 138

∴ 138 learners passed

Method II

Representing the total number of learners by a variable and solve for it.

Let n = number of learners

of means multiplication

$\frac{2}{3}$ of learners passed means

Learners who passed = $\frac{2}{3}$ x n = $\frac{\mathrm{2n}}{3}$

Total number of learners = Number of learners who failed + Number of learners who passed

Number of learners who failed = Total number of learners - Number of learners who passed

But:

Total number of learners = n

Number of learners who passed = $\frac{\mathrm{2n}}{3}$

Number of learners who failed = n - $\frac{\mathrm{2n}}{3}$

But Number of learners who failed = 69

n - $\frac{\mathrm{2n}}{3}$ = 69

Solve for n

Get rid of the fraction by multiplying both sides by the denominator, 3

n x 3 - $\frac{\mathrm{2n}}{3}$ x 3 = 69 x 3

3n - 2n = 69 x 3

n = 69 x 3

Note: Since calculators are not allowed, leave the multiplication as it is for easier cancellation later.

But number of learners who passed = $\frac{\mathrm{2n}}{3}$

Number of learners who passed = $\frac{\mathrm{2\; x\; 69\; x\; 3}}{3}$ = 2 x 69 = 138

Alternatively,

3n - 2n = 69 x 3

n = 69 x 3 = 207

Total number of learners = 207

Number of learners who passed = Total number of learners - Number of learners who failed

Number of learners who passed = 207 - 69 = 138

3a²b - 9ab² = 3a²b - 9ab²

Factorization means bring out the common terms outside the bracket and leave the rest in the bracket.

a² = a x a

3a²b = 3 x a x a x b

Since there is 3 and 3 can go into 9, express 9 as 3 x 3

b² = b x b

9ab² = 3 x 3 x a x b x b

3a²b - 9ab² = 3 x a x a x b - 3 x 3 x a x b x b

Bring out common terms outside the bracket.

3a²b - 9ab² = 3ab(a - 3b)

Length = 5 m

Volume of cube = 5 m x 5 m x 5 m

Volume of cube = 25 x 5 m³ = 125 m³

Method I

Using formula

Cost Price = $\frac{126}{\mathrm{100\%\; +\; 20\%}}$ x 100%

Cost Price = $\frac{126}{\mathrm{120\%}}$ x 100% = 105

Notes:

1. The % cancel out
2. The zeros in 120 and 100 cancel out
3. 2 divides 10, 5 times and 12, 6 times
4. 6 divides itself 1 time and 126, 21 times
5. 21 x 5 = 105

∴ Cost Price = GH₵ 105.00

Method Ii

Using proportionality

100% represents the cost price.

Selling Price = Cost Price + Profit

Selling Price% = Cost Price% + Profit%

Profit% = 20%

Cost Price% = 100%

Selling Price% = 100% + 20%

Selling Price% = 120%

Selling Price = 126

100% represents Cost Price

If 120% = 126

100% = $\frac{\mathrm{100\%\; x\; 126}}{\mathrm{120\%}}$ = 105

∴ Cost Price = GH₵ 105.00

0.000437 = 0.⌒0⌒0⌒0⌒437 = 4.37 x 10^-4

Note: the power is - 4 because we had to move the decimal point to the right 4 times.

Method I

Using formula

Let s = sales

Commission% = 15%

Commission = GH₵ 60

$\frac{15}{100}$ x s = 60

Solve for s

Get rid of the fraction by multiplying both sides by the denominator, 100

100 x $\frac{15}{100}$ x s = 60 x 100

15 x s = 60 x 100

Divide both sides by 15

s = $\frac{\mathrm{60\; x\; 100}}{15}$ = 4 x 100 = 400

Notes:

1. 15 divides itself 1 time and 60, 4 times
2. 4 x 100 = 400

∴ sales = GH₵ 400

Method II

Using proportionality

100% represents the sales

Commission% = 15%

Commission received = 60

If 15% = 60

100% = $\frac{\mathrm{100\%\; x\; 60}}{\mathrm{15\%}}$ = 400

∴ sales = GH₵ 400

$\sqrt{\mathrm{75}}$ = $\sqrt{\mathrm{25\; x\; 3}}$ = $\sqrt{\mathrm{25}}$ x $\sqrt{3}$ = 5 x $\sqrt{3}$ = 5$\sqrt{3}$

Notes:

1. 25 is a perfect square, hence 75 is expressed as 25 x 3
2. Root of a perfect square is a number when multiplied by itself gives the perfect square. 5 x 5 = 25. Hence root of 25 is 5

$\sqrt{\mathrm{18}}$ = $\sqrt{\mathrm{9\; x\; 2}}$ = $\sqrt{9}$ x $\sqrt{2}$ = 3 x $\sqrt{2}$ = 3$\sqrt{2}$

$\sqrt{\mathrm{75}}$ - $\sqrt{\mathrm{18}}$ - $\sqrt{3}$ + $\sqrt{2}$ = 5$\sqrt{3}$ - 3$\sqrt{2}$ - $\sqrt{3}$ + $\sqrt{2}$

Group like terms

$\sqrt{\mathrm{75}}$ - $\sqrt{\mathrm{18}}$ - $\sqrt{3}$ + $\sqrt{2}$ = 5$\sqrt{3}$ - $\sqrt{3}$ - 3$\sqrt{2}$ + $\sqrt{2}$

Note: treat the roots just as you will treat variables (x)

$\sqrt{\mathrm{75}}$ - $\sqrt{\mathrm{18}}$ - $\sqrt{3}$ + $\sqrt{2}$ = 4$\sqrt{3}$ - 2$\sqrt{2}$

Note: 5$\sqrt{3}$ - $\sqrt{3}$ - 3$\sqrt{2}$ + $\sqrt{2}$ is similar to 5x - x - 3y + y which gives 4x - 2y

Number of letters = 5

Number of P in HAPPY = 2

P(P) = $\frac{2}{5}$

$\left(\begin{array}{c}\mathrm{x}\\ \mathrm{y}\end{array}\right)$ → $\left(\begin{array}{c}\mathrm{x}\\ \mathrm{y\; -\; 2}\end{array}\right)$

If you observe the transformation, you will realize that the x coordinate is maintained and 2 is subtracted from the y coordinate.

(2, -3) → (2, -3 - 2)

(2, -3) → (2, -5)

A square has 4 equal sides/lengths.

The perimeter of a square = 4 x Length

Area of a square = Length x Length

Area of the square = 144 cm²

Length x Length = 144 cm²

12 x 12 = 144

Length = 12 cm

Perimeter of the square = 4 x 12 cm = 48 cm

The perimeter of the square = The perimeter of the equilateral triangle = 48 cm

Since equilateral triangle has 3 equal sides, the perimeter of the equilateral triangle = 3 x each side

3 x length of a side = 48 cm

Divide both sides by 3

Length of a side = $\frac{\mathrm{48\; cm}}{3}$ = 16 cm

7 - 2x > 15 - 4x

1. Move the x to the left side of the inequality (>) and the rest to the right.
2. When -4x moves to the left, it becomes +4x
3. When 7 moves to the right, it becomes -7
4. Simplify

4x - 2x > 15 - 7

2x > 8

Divide both sides by 2

x > $\frac{8}{2}$

x > 4

Note: since we didn't divide by negative, the inequality sign (>) remains the same.

Method I

Using formula

Total mangoes = 20

Percentage rotten = 20%

Number rotten = $\frac{20}{100}$ x 20 = 2 x 2 = 4

Notes:

1. The zeros in 100 and 20 cancel each other
2. The zeros in 10 and 20 cancel each other
3. 2 x 2 = 4

Number rotten = 4

Number not rotten = Total mangoes - Number rotten

Total mangoes = 20

Number not rotten = 20 - 4

Number not rotten = 16

Alternatively,

100% represents the total mangoes

20% rotten

Percentage not rotten = 100% - 20% = 80%

Number not rotten = $\frac{80}{100}$ x 20 = 8 x 2 = 16

Notes:

1. Zeros in 100 and 20 cancel each other
2. Zeros in 10 and 80 cancel each other
3. 8 x 2 = 16

Method II

Using proportionality

100% represents the total mangoes

20% rotten

Percentage not rotten = 100% - 20% = 80%

Total number of mangoes = 20

If 100% = 20

80% = $\frac{\mathrm{80\%\; x\; 20}}{\mathrm{100\%}}$ = 8 x 2 = 16

∴ 16 mangoes not rotten

Total number of oranges shared = Number of learners x Number each received

Total number of oranges shared = 42 x 11

Note: for easy cancellation later, leave the multiplication as it is.

Since 22 learners shared the same number of oranges:

Oranges shared by the 22 learners = 42 x 11

Number received by each learner = $\frac{\mathrm{Total\; number\; of\; oranges}}{\mathrm{Number\; of\; learners}}$

Number received by each learner = $\frac{\mathrm{42\; x\; 11}}{22}$ = 21

Notes:

1. 11 divides itself 1 time and 22, 2 times
2. 2 divides itself 1 and 42, 21
3. 21 x 1 = 21

p = $\frac{\mathrm{r\; -\; 4y}}{3}$

Get rid of the fraction by multiplying both sides by the denominator, 3

3 x p = $\frac{\mathrm{r\; -\; 4y}}{3}$ x 3

3p = r - 4y

Move the y to the left and p to the right. Negative becomes positive and positive, negative

4y = r - 3p

Divide both sides by 4

y = $\frac{1}{4}$(r - 3p)

P = {1, 2, 3, 4, 5, ... 10}

P = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Total number of numbers (samples) = 10

Set of numbers greater than 3 = {4, 5, 6, 7, 8, 9, 10}

Number of numbers greater than 3 (Possible selection) = 7

P(>3) = $\frac{7}{10}$

Interest paid = GH₵ 30

Time = 4 years

Rate = 3%

Amount borrowed is the principal.

$\frac{\mathrm{Principal\; x\; 4\; x\; 3}}{100}$ = 30

Get rid of the fraction by multiplying both sides by the denominator , 100

$\frac{\mathrm{Principal\; x\; 4\; x\; 3}}{100}$ x 100 = 30 x 100

Principal x 4 x 3 = 30 x 100

Divide both sides by 4 x 3

Principal = $\frac{\mathrm{30\; x\; 100}}{\mathrm{4\; x\; 3}}$ = 10 x 25 = 250

Notes:

1. 3 divides itself 1 time and 30, 10 times
2. 4 divides itself 1 time and 100, 25 times
3. 10 x 25 = 250

∴ amount borrowed = GH₵ 250.00

Method I

Using formula

Distance covered by 20 km/h in 35 minutes = 20 km/h x 35 minutes

Make time the subject in the speed formula.

Distance = Speed x Time

Divide both sides by Speep

Time = $\frac{\mathrm{Distance}}{\mathrm{Speed}}$

New speed = 28 km/h

Same distance = 20 km/h x 35 minutes

Time = $\frac{\mathrm{20\; km/h\; x\; 35\; minutes}}{\mathrm{28\; km/h}}$ = 25 minutes

Notes:

1. km/h cancel out
2. 4 divides 20, 5 times and 28, 7 times
3. 7 divides itself 1 and 35, 5 times
4. 5 x 5 = 25

Method II

Since distance (speed x time) is the same:

Speed₁ x Time₁ = Speed₂ x Time₂

Speed₁ = 20 km/h

Time₁ = 35 minutes

Speed₂ = 28 km/h

Substituting into the equation:

20 km/h x 35 minutes = 28 km/h x Time₂

Divide both sides by 28 km/h

Time₂ = $\frac{\mathrm{20\; km/h\; x\; 35\; minutes}}{\mathrm{28\; km/h}}$ = 25 minutes

Note: Speed and time are inversely proportional when the distance is constant. If speed increases, the travel time decreases.

Hence you can't use the direct proportionality to obtain the time. Using proportionality gives you 49 minutes which is incorrect

41 has only two factors (1 and itself) hence a prime number and not a composite number.

In order words, no other number can divide 41 without a remainder except 1 and 41.

Factors of 24 = {1, 2, 3, 4, 6, 8, 12, 24}

Factors of 39 = {1, 3, 13, 39}

Factors of 65 = {1, 5, 13, 65}

Total birds = 150

Birds sold = 26

Birds kept = 150 - 26 = 124

Number of cages = 4

Birds in each cage = $\frac{\mathrm{Birds\; kept}}{\mathrm{Number\; of\; cages}}$ = $\frac{124}{4}$ = 31

Change the ratio to fraction form:

$\frac{\mathrm{x\; +\; 2}}{\mathrm{x\; -\; 2}}$ = $\frac{1}{2}$

Cross multiply:

2(x + 2) = 1(x - 2)

2x + 4 = x - 2

2x - x = -2 - 4

x = -6

Note: in an examination, always check your answer by substituting it back into the original equation if you have enough time.

Verification

Substituting x = -6 into the original ratio:

(-6 + 2) : (-6 - 2) = -4 : -8 = 1 : 2

Notes:

1. The negatives cancel out
2. 4 divides itself 1 and 8, 2 times

∴ The answer is correct.

µ = {1, 2, 3, ... 10}

µ = {1, 2, 3,4, 5, 6, 7, 8, 9, 10}

M = {2, 3, 5, 7}

Members in µ that are not in M = {1, 4, 6, 8, 9, 10}

Express both sides of equation to have the same base:

Since the least base is 2, express 8 as a power of 2:

8 = 2 x 2 x 2 = 2³

2^2m = 2³

Since the bases are the same, the exponents must be equal:

2m = 3

Divide both sides by 2

m = $\frac{3}{2}$

m = 1.5

Fraction of the whole pocket money = 1

Fraction remains = 1 - Fraction spent

Fraction spent = Fraction spent on books + Fraction spent on pens

Fraction spent = $\frac{1}{4}$ + $\frac{1}{3}$

Fraction spent = $\frac{\mathrm{1\; x\; 3\; +\; 1\; x\; 4}}{12}$

Fraction spent = $\frac{\mathrm{3\; +\; 4}}{12}$

Fraction spent = $\frac{7}{12}$

Fraction remains = 1 - $\frac{7}{12}$

Every whole number is being divided by 1 but it is no written as a fraction with denominator 1

1 = $\frac{1}{1}$

Fraction remains = $\frac{1}{1}$ - $\frac{7}{12}$

Fraction remains = $\frac{\mathrm{1\; x\; 12\; -\; 7\; x\; 1}}{12}$

Fraction remains = $\frac{\mathrm{12\; -\; 7}}{12}$

Fraction remains = $\frac{5}{12}$

25% = $\frac{25}{100}$ = $\frac{1}{4}$

Note: 25 divides itself 1 time and 100, 4 times.

Note: If the mapping has equal interval (difference) for the y and x interval of 1, you can use the general linear sequence formula to find the rule of the mapping.

U_n = U₁ + (n-1)d

In the mapping, U_n = y and n = x and U₁ is the value of y when x = 1

U₁ = 3

y = 3 + (x-1)d

The d is the interval between each consecutive y

In this mapping, d = 6-3 = 9-6 = 12-9 = 15-12 = 3

We can substitute our d and simplify the expression for y

y = 3 + (x-1)(3)

y = 3 + 3(x) -1(3)

y = 3 + 3x - 3

y = 3x

y → 3x

Notes:

1. If you decide to substitute values for x for each of the options provided, check for all values of x.
2. Just checking once won't be sufficient.
3. For example, in x → 4 - x, substituting x = 1 gives 4 - 1 = 3, which matches the first value in the mapping but not the others hence it is not the correct rule.
4. Likewise, in x → x + 2, substituting x = 1 gives 1 + 2 = 3, which matches the first value in the mapping but not the others hence it is not the correct rule.

Use the area to find the radius:

Area = 100π cm²

100π = πr²

Get rid of π by dividing both sides by π

100 = r²

Express 10 as a square: 100 = 10²

10² = r²

Since the powers are equal, the bases must be equal: 10 = r

Therefore, the radius is 10 cm.

Substitute the radius into the circumference formula:

Circumference = 2 x π x 10 cm

Circumference = 20π cm

The horizontal lines are parallel.

The marks on sides of triangle indicate the triangle has two sides equal (Isosceles)

Isosceles triangle has base angles equal

a = b

b = 56° (Alternate angles of parallel lines)

But a = b = 56°

Sum of angles in a triangle = 180°

a + b + 2y = 180°

56° + 56° + 2y = 180°

112° + 2y = 180°

2y = 180° - 112°

2y = 68°

Divide both sides by 2

y = $\frac{68}{2}$

y = 34°

The sequence is an arithmetic progression since the difference between consecutive terms is constant.

Common difference = -5 - (-9) = 7 - 3 = 11 -7 = 4

Each consecutive term is obtained by adding the common difference to the previous term.

m = -5 + 4 = -1

8 appears three times, more than any other value.

a = $\left(\begin{array}{c}3\\ 1\end{array}\right)$ and b = $\left(\begin{array}{c}-2\\ 1\end{array}\right)$

6b + 2a = 6$\left(\begin{array}{c}-2\\ 1\end{array}\right)$ + 2$\left(\begin{array}{c}3\\ 1\end{array}\right)$

The number outside multiplies each element inside.

6b + 2a = $\left(\begin{array}{c}\mathrm{-2\; x\; 6}\\ \mathrm{1\; x\; 6}\end{array}\right)$ + $\left(\begin{array}{c}\mathrm{3\; x\; 2}\\ \mathrm{1\; x\; 2}\end{array}\right)$

6b + 2a = $\left(\begin{array}{c}-12\\ 6\end{array}\right)$ + $\left(\begin{array}{c}6\\ 2\end{array}\right)$

Add the corresponding elements. Top row to top row, bottom row to bottom row.

6b + 2a = $\left(\begin{array}{c}\mathrm{-12\; +\; 6}\\ \mathrm{6\; +\; 2}\end{array}\right)$

6b + 2a = $\left(\begin{array}{c}-6\\ 8\end{array}\right)$

p²(q - 1) = p²(q - 1)

p = 2 and q = $\frac{3}{4}$

Substitute the values:

p²(q - 1) = (2)²($\frac{3}{4}$ - 1)

2² = 2 x 2 = 4

Every whole number is being divided by 1 but not written as a fraction.

1 = $\frac{1}{1}$

p²(q - 1) = 4($\frac{3}{4}$ - $\frac{1}{1}$)

p²(q - 1) = 4($\frac{\mathrm{3\; x\; 1\; -\; 1\; x\; 4}}{4}$)

p²(q - 1) = 4($\frac{\mathrm{3\; -\; 4}}{4}$)

p²(q - 1) = 4($\frac{-1}{4}$)

p²(q - 1) = 4 x $\frac{-1}{4}$

p²(q - 1) = $\frac{\mathrm{4\; x\; -1}}{4}$

p²(q - 1) = $\frac{-4}{4}$

p²(q - 1) = -1

Method I

Using formula

Respectively means the ratios are in the order of the names mentioned.

Ivy's ratio = 3

Abbey's ratio = 2

Sum of ratios = 3 + 2 = 5

Abbey's share = $\frac{2}{5}$ x GH₵ 30.00 = GH₵ 12.00

Notes:

1. 5 divides itself 1 time and 30, 6 times.
2. 2 x 6 = 12

∴ Abbey's share is GH₵ 12.00

Method II

Using proportionality

The sum of ratios represents the total amount shared

Abbey's ratio is 2

If 5 = 30

2 = $\frac{\mathrm{2\; x\; 30}}{5}$ = 2 x 6 = 12

∴ Abbey's share is GH₵ 12.00

To find the median, we need to arrange the marks in order and find the middle value.

Marks scored by the learners are:

0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5

Note: the frequency shows how many times each mark was scored. For example, the mark 2 was scored 7 times, so we write 2 seven times.

There are 22 marks in total.

Locate the middle value(s). When there are two middle values, add them and divide by 2.

Middle values are the 11th and 12th values.

11th value = 3

12th value = 3

Median = $\frac{\mathrm{3\; +\; 3}}{2}$ = $\frac{6}{2}$ = 3

Note: if the dataset is huge, you have to use this formula to find the median position and sum the frequencies till you get to that position to use corresponding values to calculate the median.

If the position is decimal, there are two middle values and the position falls between the whole number and its next integer.

In the above case, the sum of frequencies will be:

1 + 2 + 7 + 5 + 4 + 3 = 22

Median position = $\frac{\mathrm{22\; +\; 1}}{2}$ = $\frac{23}{2}$ = 11.5

Since the position is 11.5, the middle values are the 11th and 12th values.

Sum the frequencies until you reach the 11th and 12th positions.

1 + 2 + 7 = 10

The 11th value is 3, and the 12th value is 3.

Median = $\frac{\mathrm{3\; +\; 3}}{2}$ = $\frac{6}{2}$ = 3

Number of possible selection = frequency of mark 2 = 7

Number of samples = total number of marks = 22

P(2) = $\frac{7}{22}$

$\frac{3}{4}$x = 2 + $\frac{1}{4}$

Get rid of the fractions by multiplying both sides by 4.

4 x $\frac{3}{4}$x = 4 x 2 + 4 x $\frac{1}{4}$

3x = 8 + 1

3x = 9

Divide both sides by 3

x = $\frac{9}{3}$

x = 3

Product means multiplication.

Let the third number be y.

6 x 3 x y = 90

18y = 90

Divide both sides by 18

y = $\frac{90}{18}$

y = 5

x - 5(3 - 2x) - 12x + 7 = x - 5(3 - 2x) - 12x + 7

Expand the brackets:

x - 15 + 10x - 12x + 7 = x - 15 + 10x - 12x + 7

Note: - x - = +. -5 x -2x = +10x

Group like terms:

x - 15 + 10x - 12x + 7 = x + 10x - 12x - 15 + 7

Simplify:

x - 15 + 10x - 12x + 7 = -x - 8