Solving Compound Linear Inequalities

Solve the following compound inequality: −4x + 1 ≤ 21 and 5x + 2 < 22

• x > −5 or x ≤ 4

• x ≥ −5 or x < 4

• x > −5 and x ≤ 4

• x ≥ −5 and x < 4

3(x - 3) ≤ 2(x + 2)

• x ≤ -5

• x ≥ 5

• x ≥ 13

• x ≤ 13

Solve 24 > -3r > -9 

• -8 < r < 3

• -8 > r > 3

• r > - 8 and r > 3 

• r > -8 or r < 3

x + 8 < 3 or - 8x < -40 

• x > -5 or x < 5

• x < -5 and x > 5

• x < -5 or x > 5 

• x > -5 and x < 5 

• [-3, ∞)

• (-∞, -3]

• (3, ∞)

• (-3, ∞]

Could x = - 5 be a solution to the inequality -6 < 3x + 9 < 21?

• yes

• no 

Solve the inequality.

Solve the inequality.

Which inequality represents the solution set shown on the number line?

Answer explanation

OPEN circle: < or >

CLOSED circle: < or >

When do we have to FLIP the sign in an inequality?

• when we add or subtract a negative number on both sides

• when we multiply both sides by a negative number, ONLY

• when we divide both sides by a negative number, ONLY

• when we multiply OR divide both sides by a negative number

Answer explanation

Read carefully! :)