Solving Compound Inequalities and Applications

What inequality is graphed?

• x > 2 and x < 4

• 2 ≤ x ≤ 4

• x > 2 or x < 4

• x ≥ 2 or x ≤ 4

What inequality is graphed? 

• x > 2 and x ≤ -3
• x > 2 and x < -3
• x > 2 or x ≤ -3
• x > 2 or x < -3

Solve: -3 ≤ 2x - 1 ≤ 5

• -1 ≤ x ≤ 3

• -2 ≤ x ≤ 6

• -3 ≤ x ≤ 3

• 1 ≤ x ≤ 3

Solve: 
-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

Solve:  
3x + 2 < -4  or  4x + 4 > 24

• x < -2  or  x > 5 
• x < 2  or  x > 5
• x < -2  and  x > 5 
• x < 2  and  x > 5

Solve: 
3x + 2 < -7  or  -4x + 5 < 1

• x < -3  and  x < 1
• x < -3  and  x > 1
• x < -3  or  x < 1
• x < -3  or  x > 1

Your taxi fare is $2.50 per mile, plus a $5 fee. You have a budget of $20. Which inequality models this scenario?

• 5x + 2.50 ≤ 20

• 2.50x + 5 < 20

• 2.50x + 5 ≤ 20

• 7.50x < 20

You take a trip to the bowling alley, where each game cost $2, plus you plan to spend $10 on food.  You can spend at most $25.  Which inequality models this scenario?

• 2x + 10 ≥ 25
• 2x + 10 > 20
• 2x + 10 ≤ 25
• 2x + 10 < 25

You have $120 budgeted to rent a moving truck for 2 days. Each day is $39, plus $0.25 per mile. How many miles can you drive the truck and stay within your budget?

• 170 miles

• 168 miles

• 180 miles

• 172 miles

Four times a number, increased by 6 is greater than 22.  Which inequality models this scenario?

• 4x - 6 > 22
• 4x + 6 < 22
• 4x + 6 ≥ 22
• 4x + 6 > 22