Absolute Value Inequalities and Equations

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

Tags

CCSS.6.NS.C.7C

|x+7|=12

• x = -5, x = 19

• x = 5, x = -19

• x = 5, x = -5

• x = 12, x = -7

3| −8x| + 8 = 80

• {-7/3, 7/3}
• {-3,3}
• {11/3,-11/3}
• No Solution

8|-2x + 4| = 96

• x = -4, x = 8
• x = -4
• x = -4, x = -8
• x = 4, x = 8

Solve:
 |x + 3| > 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

Solve:
3 | 2x + 7| - 7 < -4

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution

Solve

• no solution
• all real numbers

• no solution
• all real numbers 
• -2 ≤ n ≤ 16
• n ≤ -2 or n ≥ 16

Write an inequality for Graph 3.

• x ≤ -2 AND x > 5
• x ≤ -2 OR x > 5
• x ≥ -2 OR x < 5
• -2 ≤ x < 5

Solve:
3 | 2x + 7| + 7 < 4

• x < -3 and x > -5/3
• x < -3 and x > -4
• all real numbers
• no solution