Solving Equations Absolute Value and Inequalities

|x| > 7 Is this an "and" or an "or"?

• And

• Or

|2x| ≤ 14; Is this an AND or an OR?

• AND

• OR

Solve the following compound inequality:

−8 < 2(x + 4) or −3x + 4 > x − 4

• No solutions

• x < −8 or x < 2

• x > −8 or x < 2

• x < −8 and x < 2

What is the first step?

• Get the absolute value alone by dividing both sides by 5

• Drop the absolute value bars and add 7 and 5 together

• Get the absolute value alone by subtracting 5 from both sides

Look at the graph. Write the inequality in interval notation.

• (-2,5)

• (-∞,-2)⋃(5,∞)

• [-2,5]

• (-∞,-2]∪[5,∞)

What is the solution to the absolute value equation 2|4x - 1| = 6?

• {-1/2, 1}

• {-4, 8}

• {-1}

• No Solution

What is the solution to the inequality -4|3x - 1| ≥ 8?

• ℝ

• (-∞, 9) ∪ (9, ∞)

• No Solution

• { -1 }

2x² + 5x ≥ 12 , then find the interval notation of the inequality.

• [-4, 1.5]

• (−∞, -4) U (1.5, ∞)

• (−∞, -4] U [1.5, ∞)

• no solution

1. Plot the solution set to the quadratic inequality on the number line provided.

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Which of the following is the interval notation of x² - x - 12 < 0?

• [ 4, 3]

• (-4, -3]

• (-3, 4)

• [-3, 4]