Question 1

LEVEL 4

Solve the following linear equation:

10(3-x)=5

Select the correct answer from the list below:

A: x=2

B: x=2.5

C: x=5

D: x=-2.5

CORRECT ANSWER:B: x=2.5

WORKED SOLUTION:

Expand the brackets

30-10x=5

Subtract 15 from both sides

25-10x=0

Add 10x to both sides

25=10x

Divide both sides by 10

x=\dfrac{25}{10}=2.5

Question 2

LEVEL 3

Solve the following linear equation:

2x-5=4

Select the correct answer from the list below:

A: x=9

B: x=4.5

C: x=-9

D: x=4

CORRECT ANSWER:B: x=4.5

WORKED SOLUTION:

Add 5 to both sides 2x=9

Divide both sides by x=\dfrac{9}{2}=4.5

Answer =4.5

Question 3

LEVEL 4

Solve the following linear equation:

4(5x-1)= 16

Select the correct answer from the list below:

A: x=4

B: x=3

C: x=2

D: x=1

CORRECT ANSWER: D: x=1

WORKED SOLUTION:

Expand the brackets

20x-4= 16

Add 4 to both sides

20x=20

Divide both sides by 20

x=\dfrac{20}{20}=1

Question 4

LEVEL 4

Solve the following linear equation:

7(2x-9)= 7

Select the correct answer from the list below:

A: x=5

B: x=6

C: x=4

D: x=2.5

CORRECT ANSWER:A: x=5

WORKED SOLUTION:

Expand the brackets

14x-63= 7

Add 63 to both sides

14x=70

Divide both sides by 14

x=\dfrac{70}{14}=5

Question 5

LEVEL 4

Solve the following equation:

8b^2=288

Select the correct answer from the list below:

A: b=6

B: b=2

C: b=36

D:b=3

CORRECT ANSWER:A: b=6

WORKED SOLUTION:

Divide both sides by 8.

b^2 = 36

Take the square root of both sides.

b = 6

Question 6

LEVEL 3

Solve the following linear equation:

7b-8=55

Select the correct answer from the list below:

A: b=63

B: b=9

C: b=8

D: b=7

CORRECT ANSWER: B: b=9

WORKED SOLUTION:

Add 8 to both sides

7b=55+8=63

Divide both sides by 7

b=\dfrac{63}{7}=9

Question 7

LEVEL 4

Solve the following linear equation:

\frac{3p - 28}{7} =5

Select the correct answer from the list below:

A: p=\dfrac{7}{3}

B: p=9

C: p=19

D: p=21

CORRECT ANSWER:    D: p=21

WORKED SOLUTION:

Since there is a fraction, multiply both sides by the denominator (in this case 7)

to make it fraction-less, this will mean the equation now becomes:

3p-28=35

Add 28 to both sides

3p=35+28=63 i.e. 3p=63

Divide both sides by 3

p=\dfrac{63}{3}=21

Answer = 21

An alternative method for solving this would be to

add 4 to both sides as the first step, then multiply by 7.

Question 8

LEVEL 4

Solve the following linear equation:

\dfrac{5}{8} p+3=8

Select the correct answer from the list below:

A: p=\dfrac{5}{8}

B: p=\dfrac{8}{5}

C: p=8

D: p=5

CORRECT ANSWER: C: p=8

WORKED SOLUTION:

Multiply both sides by the denominator (in this case 8)

5p+24=64

Subtract both sides by 24

5p=64-24=40

Divide both sides by 5

p=\dfrac{40}{5}=8

Question 9

LEVEL 3

Solve the following linear equation:

15s-4=5s+26

Select the correct answer from the list below:

A: s=5

B: s=3

C: s=4

D: s=10.5

CORRECT ANSWER: B: s=3

WORKED SOLUTION:

Subtract 5s from both sides

10s-4=26

Add 4 on both sides

10s=30

Divide both sides by 10

s=\dfrac{30}{10}=3