Solving Absolute Equations and Inequalities

Solve:
|2x-3|=5

• x=4
• x=4 and x=-4
• x=4 and x=-1
• x=14

Solve:
2|5x-1|+3=9

• x=4/5
• x=7/5 and x=-1
• x=7/5
• x=4/5 and x=-2/5

Solve:
 |−2n| + 10 = −50

• {30, -30}
• {20,-20}
• {-5,5}
• No Solution

When you graph an inequality, you used a closed dot when you use which symbols?

• ≤, ≥ 
• <, >

Solve:
|x + 4| - 8 > 2

• x > 6 and x < 10
• x > 6 or x < -14
• all real numbers
• no solution

What kind of inequality is this? |x-2|<7

• AND compound inquality
• OR compound inequality

• r > 11/4 or r < 9/4
• r > 5 or r ≤ 0
• r > 5 or r < 0
• r < -5 or r > 0

The radius of the gears produced at a factory must be 6 inches in length with a tolerance of 0.1 inches. The gears with radius beyond the tolerated lengths will be thrown away. Which of the following inequalities can be used to assess which gears are eligible? (x is the length of the radius)

• |x – 6| ≤ 0.1
• |x – 6| ≥ 0.1
• |x – 0.1| ≤ 6
• |x – 0.1| ≥ 6

The lowest test grade in a class is a 75 and the highest is 91. What is the allowance of grade from the median grade?

• 75 points
• 91 points
• 8 points
• 83 points