Solve Equations Absolute Value

Solve for x:

∣ x + 6 ∣ - 3 = 3x + 11

• S = { 2 }

• S = { -5, -4 }

• S = { -5 }

• S = { -4 }

Solve the inequality.

|m| + 5 < 9

• (-∞, 4)

• (-∞, -4)

• (-4, 4)

• [-4, 4]

Solve the inequality.

|x + 4| - 8 > 2

• (6, 10)

• (-∞, -14) U (6, ∞)

• (-∞, ∞)

• ∅

Solve the inequality.

| x + 3 | ≤ 2

• [ 1, 5 ]

• [ -5, -1 ]

• (-∞, ∞)

• ∅

Harry Styles keeps as little as £100 and at most £290 in his savings account. Write an absolute value inequality to represent Harry's savings account balance, s.

• | s - 195 | ≤ 95

• | s - 195 | ≥ 95

• | s + 195 | ≥ 95

• | s + 195 | ≤ 95

Solve:

| x - 20 | = -3

• S = { 17 }

• S = { 17, 23 }

• (-∞, ∞)

• ∅

Rewrite the following solutions as an absolute value inequality:

-12 ≤ x ≤ 4

• | x + 4 | ≤ 8

• | x - 4 | ≤ 8

• | x - 8 | ≤ 4

• | x + 8 | ≤ 4

Choose the best definition of 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

• No Solution

• - 7 < y < 3
• - 8 < y < 4
• - 7 < y < - 3
• - 8 < y < - 4