Solving Absolute Value Equations Quiz

If |x| = 15, what are the possible values of x?

• 15 and -1

• 15 and 0

• 15 and -15

• 15 and 1

Answer explanation

The equation |x| = 15 means x can be either 15 or -15, as absolute value represents distance from zero. Therefore, the correct possible values of x are 15 and -15.

Solve the absolute value equation: |x + 4| = 11. What are the solutions?

• x = 7 or x = -15

• x = 8 or x = -12

• x = 11 or x = -11

• x = 15 or x = -7

Answer explanation

To solve |x + 4| = 11, we set up two equations: x + 4 = 11 and x + 4 = -11. Solving these gives x = 7 and x = -15. Thus, the solutions are x = 7 or x = -15.

Solve the following equation:

|−2n| + 10 = −50

• {30, −30}

• {20, −20}

• {−5, 5}

• No Solution

Answer explanation

The equation |−2n| + 10 = −50 has no solution because the absolute value |−2n| is always non-negative, making the left side at least 10. Thus, it can never equal a negative number like −50.

Evaluate each expression.
| x + 9 | = -5

• -14

• -4

• {-14, -4}

• no solution

Answer explanation

The expression |x + 9| represents the absolute value, which cannot equal a negative number. Since -5 is negative, there are no values of x that satisfy the equation, leading to the conclusion of 'no solution'.

Is x = -5 a solution to the equation |3x + 22| = 6?

• Yes, because |-7| = 5

• No, because |-7| = 7

• Yes, because |-7| = 6

• No, because |-7| = 8

Answer explanation

To check if x = -5 is a solution, substitute it into the equation: |3(-5) + 22| = | -15 + 22| = |7|. Since |7| does not equal 6, x = -5 is not a solution. Thus, the correct answer is 'No, because |-7| = 7'.

Solve the absolute value equation: |2x| = 9. What are the solutions?

• x = 5 or x = -5

• x = 3 or x = -3

• x = 4 or x = -4

• x = 4.5 or x = -4.5

Answer explanation

To solve |2x| = 9, we set up two equations: 2x = 9 and 2x = -9. Solving these gives x = 4.5 and x = -4.5. Thus, the correct solutions are x = 4.5 or x = -4.5.

Determine if x = 9 is a solution to the equation |x - 7| = 16.

• Yes, because |9 - 7| = 16

• No, because |9 - 7| = 2

• No, because |9 - 7| = 1

• Yes, because |9 - 7| = 9

Answer explanation

To check if x = 9 is a solution, calculate |9 - 7|. This equals |2|, which is 2, not 16. Therefore, x = 9 is not a solution to the equation |x - 7| = 16. The correct choice is 'No, because |9 - 7| = 2'.

| x – 3 |= 0

• 3

• -3

• {-3, 3}

• no solution

Answer explanation

To solve |x - 3| = 0, we set the expression inside the absolute value to zero: x - 3 = 0. This gives us x = 3. Thus, the correct answer is 3.

Solve the absolute value equation: |1/2x + 3| = 9. What are the solutions?

• x = 14 or x = -28

• x = 10 or x = -20

• x = 12 or x = -24

• x = 16 or x = -32

Answer explanation

To solve |1/2x + 3| = 9, set up two equations: 1/2x + 3 = 9 and 1/2x + 3 = -9. Solving these gives x = 12 and x = -24. Thus, the correct solutions are x = 12 or x = -24.

Solve the absolute value equation: |6x - 11| + 2 = 41. What are the solutions?

• x = 25/3 or x = -14/3

• x = 35/3 or x = -20/3

• x = 20/3 or x = -10/3

• x = 30/3 or x = -15/3

Answer explanation

To solve |6x - 11| + 2 = 41, first isolate the absolute value: |6x - 11| = 39. This gives two equations: 6x - 11 = 39 and 6x - 11 = -39. Solving these, we find x = 25/3 or x = -14/3, which matches the correct choice.