Question

Time remaining 01:58:53 which equation has only one solution?

a. |x – 5| = –1
b. |–6 – 2x| = 8
c. |5x 10| = 10
d. |–6x 3| = 0

Answer 1

The equation from the choices provided that has only one solution is d. |–6x + 3| = 0 because an absolute value equals zero only when the expression inside the absolute value is also zero.

Step-by-step explanation:

The question asks which equation has only one solution. To determine this, we analyze each equation:

• a. |x – 5| = –1: This equation has no solution because the absolute value cannot be negative.
• b. |–6 – 2x| = 8: This equation could potentially have two solutions because it can be set up as two separate equations (–6 – 2x = 8 or –6 – 2x = –8).
• c. |5x + 10| = 10: This equation also could potentially have two solutions (5x + 10 = 10 or 5x + 10 = –10).
• d. |–6x + 3| = 0: This equation has exactly one solution because the only way the absolute value equals zero is if the expression inside is zero, which gives a single solution when solved.

Therefore, the equation that has only one solution is d. |–6x + 3| = 0.