Question

Gwendolyn is asked to solve the equation –4(x – 3) = 20. She shows the work below and states that the solution is x = –8. –4(x – 3) = 20 –4x + 12 = 20 –4x = 32 x = –8 Unfortunately, Gwendolyn's work is flawed. Explain the flaw in Gwendolyn's work. Determine the correct solution to the equation.

Answer 1

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Explanation:

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Answer 2

`x=-2`

Explanation:

Given: Equation is
`-4(x-3)=20`

To find: flaw in Gwendolyn's work and the correct solution to the equation.

Solution:

In the given question,

the first step is
`-4(x-3)=20`

The second step is
`-4x+12=20`

(This step is obtained on multiplying
`-4` by
`x-3`)

The third step is
`-4x=32`

This step is wrong as on transposing 12 from left side of the equation in the second step to the right side, the following equation is obtained:

`-4x=20-12\\-4x=8\\x=-2`

So, the correct solution is
`x=-2`