Question

Trish is solving the equation x + 10 = 8 for the value of x.

x + 10 + 10 = 8 + 10
x = 18
(2)x = (2)18
x = 36
What error did Trish make?





What is the correct value of x?

Answer 1

Trish made an error in her calculations when she attempted to manipulate the equation. Let's walk through her steps and identify the mistake:

1. Starting with the original equation:
\[
x + 10 = 8
\]

2. She added 10 to both sides:
\[
x + 10 + 10 = 8 + 10
\]
Simplifying this gives:
\[
x + 20 = 18
\]

3. Trish claims that \( x = 18 \), but this is incorrect. The correct next step would be to isolate \( x \) as follows:
\[
x + 20 - 20 = 18 - 20
\]
Simplifying further:
\[
x = -2
\]

Instead, Trish incorrectly proceeded to multiply both sides by 2:
4. \( (2)x = (2)18 \) which means \( 2x = 36 \).

5. This step is an incorrect transformation of the equation.

The correct value of \( x \) is:
\[
x = -2
\]