Equations Containing Brackets

To solve equations with brackets: 

(i) Remove or expand the brackets 
(ii) Collect letters on one side and numbers on the other side 
(iii) Solve the equation as usual 

Example 6.2.1:

Solve the following equations: 

a. 2(5x – 1) = 22 

b. 2(x – 2) = 4x – 5 

c. 5(k – 3) + 2(k – 4) = 19 

Solution 

a. 2(5x – 1) = 22 

Remove brackets 

2(5x) + 2(-1)  = 22 

10x – 2 = 22 

Collect like terms 

10x = 22 + 2 

10x = 24 

Divide both sides by 10 

\( \frac{10x}{10} = \frac{24}{10}\)

\( \scriptsize x = \normalsize \frac {24}{10} \)

\( \scriptsize x = \normalsize \frac {12}{5} \)

\( \scriptsize x = 2 \frac {2}{5} \)

b. 2(x – 2) = 4x – 5 

Remove brackets 

2(x) + 2(-2) = 4x – 5 

2x – 4 = 4x – 5 

Collect like terms 

2x – 4x = -5 + 4

-2x = -1 

Divide both sides by -2 

\( \frac{-2x}{-2} = \frac{-1}{-2} \)

\( \scriptsize x = \normalsize \frac{-1}{-2} \)

\( \scriptsize x = \normalsize \frac{\not{-}1}{\not{-}2} \)

\( \scriptsize – \: \div \: – \: = \: + \)

∴ \( \scriptsize x = \normalsize \frac{1}{2} \)

c. 5(k – 3) + 2(k – 4) = 19 

Remove brackets 

5(k) + 5(-3) + 2(k) + 2(-4) = 19 

5k – 15 + 2k – 8 = 19 

Re-arrange

5k + 2k – 15 – 8 = 19 

7k – 23 = 19 

Collect like terms 

7k = 19 + 23  

7k = 42 

Divide both sides by 7 

\( \frac{7k}{7} = \frac{42}{7} \)

\( \scriptsize k = \normalsize \frac{42}{7} \)

\( \scriptsize k = 6 \)

Evaluation Questions: