Question

Josefina started to solve for x in the equation
3.5 = 1.9 – 0.8|2x – 0.6| using the steps below:
3.5 = 1.9 – 0.8|2x – 0.6|
1.6 = –0.8|2x – 0.6|
–2 = |2x – 0.6|
Why did Josefina stop at Step 3?

Answer 1

      She stopped because the equation has no solution. Absolute value on the right side of the equation is always positive  ( the non-negative value) and there is result -2 on the left side of equation.
      x  ∈ ∅

Answer 2

The reason Josefina stopped at Step 3 is because the equation has no solution. -2 = |2x - 0.6| is false.

Recall:

• Absolute value of a number is the positive value of that number. i.e. absolute value of -a is |-a| = a.
• In an equation, the right side must be equal to a right side. If the right does not tally with the left side, such equation has no solution.

Given that Josefina stopped in step 3 at:

• -2 = |2x - 0.6| (this equation is false).

Since the left has a negative value, the right should also have a negative value.

Therefore, the reason Josefina stopped at Step 3 is because the equation has no solution. -2 = |2x - 0.6| is false.

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