Question

Misha found that the equation –|2x – 10| – 1 = 2 had two possible solutions: x = 3.5 and x = –6.5. Which explains whether or not her solutions are correct?

Answer 1

Misha's solution is incorrect since the equation has no solution.

Explanation:

There is no value of x that can make the left side positive, so there is no solution for this equation, and Misha's solution must be incorrect.

Answer 2

See below.

Explanation:

Misha's solution is incorrect since the equation has no solution.

The value that comes out of any absolute value, such as |2x - 10|, is non-negative. That means it can only be zero or positive. If the value of |2x - 10| is zero, then -|2x - 10| is still zero, and -|2x - 10| - 1 is negative. It cannot equal 2.

If what comes out of |2x - 10| is positive, then -|2x - 10| is negative, and the value of -|2x - 10| - 1 is also negative. It cannot equal 2.

There is no value of x that can make the left side positive, so there is no solution for this equation, and Misha's solution must be incorrect.