Question

analyzing the procedure used to solve an absolute value
josefina started to solve for x in the equation
3.5 = 1.9 - 0.8|2x - 0.6| using the steps below:

1. 3.5 = 1.9 - 0.8|2x - 0.6|
2. 1.6 = -0.8|2x - 0.6|
3. -2 = |2x - 0.6|

why did josefina stop at step 3?

Explanation:

The absolute - value of a number is always non - negative. In Step 3, the left - hand side is negative (-2) while the right - hand side is an absolute value expression \(|2x - 0.6|\) which must be non - negative. So, there is no solution for the equation, and that's why Josefina stopped.

Answer:

There is no solution to the equation because the absolute - value of a number cannot equal a negative number. The left - hand side of the equation in Step 3 is negative (-2), while the right - hand side \(|2x - 0.6|\) is non - negative.