Everything Maths Grade 10

Step 2: Rearrange and solve forq

4 q+ 3< 2 q+ 6

4 q 2 q < 6  3

2 q < 3

Step 3: Divide both sides by 2

2 q < 3

q <

3

2

Step 4: Represent the answer on a number line

0 1 2 3 4 5

q<^32

Step 5: Represent the answer in interval notation
(
1;^32

)

Worked example 19: Solving compound linear inequalities

QUESTION

Solve forx:

5 x+ 3< 8

Represent the answer on a number line and in interval notation.

SOLUTION

Step 1: Subtract 3 from all the parts of the inequality

5  3  x+ 3 3 < 8  3

2  x < 5

Step 2: Represent the answer on a number line

0 1 2 3 4 5 x

2  x< 5

Step 3: Represent the answer in interval notation

[2; 5)

Chapter 4. Equations and inequalities 99