Absolute Value Inequalities Algebra Two

Solve:
 |x + 3| > 8

• x > 5 or x < -11

• x > 5

• all real numbers

• no solution

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Or

Solve.
|c + 4| < 5

• x < -9 or x > 1

• -9 < x < 1

• x < 9 or x > -1

• -1 < x < 9

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And

Solve.
|y - 4| ≥ 8

• y ≤ -4 or y ≥ 12

• -4 ≤ y ≤ -12

• y ≤ 4 or y ≥ -12

• -12 ≤ x ≤ 4

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Or

Solve.
|y - 1| ≤ 6

• -7 ≤ y ≤ 5

• y ≤ -7 or y ≥ 5

• -5 ≤ y ≤ 7

• y ≤ -5 or y ≥ 7

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And

Solve.
|5x + 7| < 22

• x < -5 ⅘ or x > 3

• -5 ⅘ < x < 3

• -3 < x < 5 ⅘

• x < -3 or x > 5 ⅘

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And

Solve.
6 - 2|m -3| > -4

• -8 < m < 2

• m < -8 or m > 2

• m < -2 or m > 8

• -2 < m < 8

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Or

Solve for v.

• v ≥ -6 and v ≤ -4

• v > -6 and v < -4

• v ≥ -6 or v ≤ -4

• v > -6 or v < -4

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And

| -8x | < 8

What is the correct first step?

• separate into two inequalities with an "and" or a between statement

• separate into two inequalities with an "or" statement

• divide both sides by -8

• add 8 to both sides

What is ALWAYS the first GOAL in solving an absolute value inequality?

• set up the positive case

• set up the negative case

• isolate the absolute value expression

• multiply or divide by the coefficient of the variable

| x + 3 | ≤ 2

• No Solution

• x ≤ -1

• -5 ≤ x and x ≤ -1

• 1 ≤ x and x ≤ 5 ... 1 ≤ x ≤ 5