# Unit 8 Section 2 : Linear Equations with Brackets

Sometimes we are given an equation with brackets in.
Usually it is best to multiply out the brackets first.

### Example Question 1

 Solve this equation: 5 ( x - 3 ) = 35 Start by multiplying out the brackets: 5x - 15 = 35 Now add 15 to both sides: 5x = 50 Finally divide by 5 on both sides: x = 10

### Example Question 2

 Gilda thinks of a number and adds 7 to it. She then multiplies her answer by 4 and gets 64. What was her original number? Start by working out the equation to solve. Let's call Gilda's original number x. Gilda added 7 to her number, which would give x+7. Then she multiplied this by 4, which would give 4(x + 7). Her answer was 64, so we now know that 4(x + 7) is equal to 64:
 4 ( x + 7 ) = 64 Start by multiplying out the brackets: 4x + 28 = 64 Now subtract 28 from both sides: 4x = 36 Finally divide by 4 on both sides: x = 9 So Gilda's original number was 9.

### Example Question 3

The area of the following rectangle is 41 cm².
5 cm
(2x+4) cm
What is the value of x?

Start by working out the equation to solve.
The area of a rectangle is found by multiplying the width and length.
In this case the width is 5 and the length is (2x+4), so the area is 5(2x+4).
We know the area is 41, so we now know that 5(2x + 4) is equal to 41:

 5 ( 2x + 4 ) = 41 Start by multiplying out the brackets: 10x + 20 = 41 Now subtract 20 from both sides: 10x = 21 Finally divide by 10 on both sides: x = 2.1 So the value of x was 2.1.

## Practice Questions

Work out the answer to each of these questions then click on the button marked to see whether you are correct.

(a) Solve the equation: 7(x+3) = 49 (b) James thinks of a number. He subtracts 2 and then multiplies by 5 and gets 45. What was his number? (c) Look at the rectangle below:
4 cm
(5x-2) cm
The area of the rectangle is 17cm².
What is the value of x? ## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

Question 1
 (a) 2(x + 6) = 14    x =  (b) 5(x - 8) = 40    x =  (c) 3(x + 5) = 12    x =  (d) 7(x + 4) = 42    x =  (e) 2(x + 7) = 19    x =  (f) 5(x + 2) = 19    x =  (g) 5(x - 4) = 12    x =  (h) 10(x + 7) = 82    x =  Question 2
 (a) 5(2x - 7) = 8    x =  (b) 3(3x + 6) = 27    x =  (c) 3(2x + 1) = 30    x =  (d) 8(2x - 12) = 24    x =  Question 3
Look at the rectangle below.
3 m
(x+4) m
The area of the rectangle is 18 m².
What is the value of x?
x =  Question 4
Feti chooses a number, adds 7, multiplies the result by 5, and gets the answer 55.
What was her original number?  Question 5
The following flowchart is used to form an equation: What is the value of x?  Question 6
 (a) 4(7 - x) = 20    x =  (b) 3(9 - x) = 15    x =  (c) 6(5 - 2x) = 18    x =  (d) 5(7 - 6x) = 20    x =  (e) 2(10 - x) = 17    x =  (f) 5(9 - 5x) = 4    x =  Question 7
Alice thinks of a number, subtracts it from 11, multiplies the result by 5, and gets the answer 45.
What was her original number?  Question 8
 (a) 2(x + 1) = 6(x - 3)    x =  (b) 3(x + 4) = 11x    x =  (c) 5(x + 4) = 2(10x + 1)    x =  (d) 4(7 - x) = 5(x + 2)    x =  