Solve Absolute Value Inequalities and Word Problems

Solve.
-5|x - 4| > 20

• x < 8 and x > 0

• x > 8 or x < 0

• all real numbers

• no solution

Solve.
-5|x - 4| < 20

• x < 8 and x > 0

• x > 8 or x < 0

• all real numbers

• no solution

Your have money in your wallet, but you don't know the exact amount. When a friend asks you, you say that you have 50 dollars give or take 15. Write an absolute value equation to model this situation.

• |x-50|=15

• |x+15|=50

• |50+x|=15

• No Solution

A company sells 20-ounce bottles of sports drink. The actual volume of liquid in the bottle must be within 0.03 ounces. What equation can be solved to find the minimum and maximum volume of liquid in a bottle.

• |v|-20=0.03

• |v-20|=0.03

• |v|-0.03=20

• |v-0.03|=20

• - 7 < y < 3
• - 8 < y < 4
• - 7 < y < - 3
• - 8 < y < - 4

• - 1/2 ≤ z ≤ 5/2
• 1/2 ≤ z ≤ 5/2
• z ≥ 1/2 or z ≤ 5/2
• z ≤ 1/2 or z ≥ 5/2

• - 4 ≤ x ≤ 6
• x ≥ - 4 or x ≤ 6
• x ≥ 4 or x ≤ - 6
• - 4 ≤ x ≤ - 6

• - 6 < x < 26/5
• - 6 < x < 25
• x < - 6 or x > 26/5
• x > - 6 or x < 26/5

• - 1/3 < n or n > 5/3
• -1/3 < n < 5/3
• 1/3 < n < 5/3
• n < -5/3 or n > 1/3

Your have money in your wallet, but you don't know the exact amount. When a friend asks you, you say that you have 50 dollars give or take 15. Write an absolute value equation to model this situation.

• |x - 50|=15

• |x + 15|=50

• |x + 50|=15

• |x - 15|=50