Question

For which equations is x = 9 a possible solution? Check all that apply.

a. lxl = 9
b. -|x| = 9
c. -|-x| = 9
d. -|-x| = -9
e. x = -9
f. |-x| = 9
g. |-x| = -9

Answer 1

Equations a, d, and f have x = 9 as a possible solution, as they satisfy the conditions set by the absolute value operation and equation equality.

Step-by-step explanation:

The student has asked to identify which equations have x = 9 as a possible solution. We will evaluate each option provided.

• a. |x| = 9: This is true when x is either 9 or -9, so x = 9 is a possible solution.
• b. -|x| = 9: This is never true because the absolute value is always non-negative, thus the negative absolute value will always be non-positive.
• c. -|-x| = 9: Similarly to option b, this is always non-positive and cannot equal positive 9.
• d. -|-x| = -9: This is true when |-x|, which is always non-negative, equals 9. And since -x can be 9 when x is -9, x = 9 is a possible solution.
• e. x = -9: This explicitly states that x is -9, so x = 9 cannot be a solution.
• f. |-x| = 9: This is true when x is -9, or 9. Hence, x = 9 is a possible solution.
• g. |-x| = -9: The absolute value cannot be negative, so this equation has no solution.

Therefore, the following equations have x = 9 as a possible solution: a, d, and f.