Question

Solve: | 2x - 2 | = x + 1

Select the appropriate response
A) x=3,x=6
B) x=3, x=1/3
C) x=9

Can you help me with this, please?

Answer 1

The given expression is
`|2 x-2|=x+1`

We need to determine the solution to the expression.

Solution:

The absolute value of the expression
`|2 x-2|=x+1` is given by

`2 x-2=x+1` or
`2 x-2=-(x+1)`

Let us solve the expression
`2 x-2=x+1`

Thus, we get;

`x-2=1`

`x=3`

Now, solving the expression
`2 x-2=-(x+1)`

Thus, we get;

`2x-2=-x-1`

`3x-2=-1`

`3x=1`

`x=(1)/(3)`

Thus, the solution of the expression is
`x=3`,
`x=(1)/(3)`

Hence, Option B is the correct answer.