1. Solving Linear Equations involving Brackets
Mathematics
Solving Linear Equations involving Brackets

2. Aims of the Lesson The aim of this powerpoint is to help you…
Revise expanding brackets
Solve simple linear equations that involve brackets.

3. Equations with Brackets
There are two ways of solving equations involving brackets…
EITHER expand the brackets first then re-arrange the equation collecting like terms together etc. before solving as you would a typical linear equation
OR if appropriate, dividing through by what’s outside the brackets and then solving the linear equation remaining

4. Revising Expanding Brackets
EACH item inside the brackets is multiplied by the value/term outside of the brackets…
5 ( x + y )  5x + 5y
3 (2 + a)  a
– 7 (2b + 5)  – 14b –35
– 2x (x – 7)  – 2x2 + 14x

5. Solving by Expanding First
Solve…
6 (3p + 2) = 84
Expanding gives…
18p + 12 = 84
Take 12 off both sides…
18p =
Divide both sides by 18…
p =
Solve…
2 (x + 3) – 5x = 24
Expanding gives…
2x – 5x = 24
Simplifying gives…
– 3x = 24
Take 6 off both sides…
– 3x = 18
Divide both sides by – 3…
x = – 6

6. Solving by Dividing First
IF dividing does not bring up fractions immediately then divide first BUT don’t forget EVERY term needs to be divided throughout the equation…

7. Examples 2 Solve… 8 (p – 5) = 48 Divide everything by 8… (p – 5) = 6
Add 5 to both sides…
p = 11
Solve…
5(3 + r) – 20 = 75
Divide everything by 5…
(3 + r) – 4 = 15
3 + r – 4 = 15
Simplify…
r – 1 = 15
Add 1 to both sides…
r = 16

8. Beware… Answers can be negative or fractional
Don’t forget when dividing by a number you could simply write it as the bottom of a fraction…
E.g. 12p = 5
Divide both sides by 12…
p = 5/12

9. What next?
Make appropriate notes (including examples) on solving linear equations involving brackets or printout the prepared notes & complete the tasks within them.
Work through the MyMaths lesson (and then its online homework) called:
Algebra > Equations Linear > Equations 4 – Brackets
Save and complete the worksheet: LinEq-S3.xlsx