Solving Compound Inequalities

a

We can solve the inequality by first subtracting $2$ from both sides and then dividing by $5 .$

12 \leq 2 + 5 x

LHS - 2 \leq RHS - 2

10 \leq 5 x

RearrangeIneqRearrange inequality

5 x \geq 10

LHS / 5 \geq RHS / 5

x \geq 2

The solution set of the inequality is $x \geq 2,$ that is, all $x$ -values greater than or equal to $2 .$

b

We solve this inequality by adding

5

on both sides and then dividing by

- 4 .

Since we divide with a negative we have to flip the inequality sign.

- 4 x - 5 \geq 7

LHS + 5 \geq RHS + 5

- 4 x \geq 12

- 4

and flip inequality sign

x \leq - 3

The inequality is true for

x \leq - 3,

meaning all

x

-values less than or equal to

- 3 .

Solving Compound Inequalities 1.2 - Solution