Solving Equations Absolute Value and Inequalities

Write an inequality for Graph 4.

• -2 < x < 5

• x < -2 or x > 5

• x ≥ -2 OR x < 5

• -2 ≤ x ≤ 5

Solve the absolute value equation. 

• {7}

• {-7, 7}

• {0, 7}

• No Solution

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

Evaluate the expression.
|1 - 5|

• 4

• -4

• -6

• 6

| x – 3 |= 0

• 3

• -3

• {-3, 3}

• no solution

Solve |2x –3| + 5 =10.

• -1, 1

• -1, 4

• -1, -4

• 1, 4

Write an inequality for Graph 2.

• −2 ≤ x < 5

• x ≤ −2 AND x > 5

• x ≥ −2 OR x < 5

• −2 ≤ x ≤ 5

What is the first step?

• Drop the absolute value bars by splitting into two equations

• Add 2 to both sides

|6 - 2k| = 18

• k = -6

• k = -6, k = 12

• k = -6, k = -12

• k = -6, k = 5

|-2 - 4n| = 34

• n = -9, n = 8

• n = 9, n = 8

• n = -9

• n = 8