Absolute Value Equations and Inequalities Concepts

Solve. 
-5|4 +n| < -15 

• n > 1 or n < -7

• n > -1 or n < -7

• -7 < n < -1

• no solution

Solve. 
| -x - 10| + 4 < -8 

• no solution

• x > 2 or x < -22

• -22 < x < 2

• all real numbers

-5|-n + 7| ≥ -45

• no solution

• all real numbers 

• -2 ≤ n ≤ 16

• n ≤ -2 or n ≥ 16

4|5x-2|+7>39

• -6/5 < x > 2

• x=2 or x=-6/5

• x=2 and x=-6/5

• x < -6/5 or x > 2

|2a - 10| = 6

• a = 8, a = 5

• a = 2

• a = 8

• a = 8, a = 2

Solve:
 |x + 3| > 8

• x > 5 or x < -11

• x > 5

• all real numbers

• no solution

|v + 8| − 5 = 2 

• {-1,-15}

• {-1,-5}

• {-15,15}

• No Solution

Evaluate each expression.
| x + 9 | = -5

• -14

• -4

• {-14, -4}

• no solution

Solve:

• {24}

• {-6, -8}

• {16, 4}

• {24, -24}

What's a way to define absolute value?

• The value of a number

• The opposite of a number

• The distance of a number from zero

• The multiplicative inverse of a number