Question

I need to solve the absolute value for |2x - 7| = |2x + 9| please anything will help thank you!!!

Answer 1

-1/2

Explanation:

One way: Since both sides have absolute value, you could square both sides to get rid of the absolute value. This will result in a possible quadratic given the degrees inside the squares; I can already tell you know in this cases the variable squares will cancel since the coefficient of x on both sides inside the | | are the same.

`(2x-7)^2=(2x+9)^2`

Expand both sides using:
`(a+b)^2=a^2+2ab+b^2`.

`4x^2-28x+49=4x^2+36x+81`

Subtract
`4x^2` on both sides:

`-28x+49=36x+81`

Add
`28x` on both sides:

`49=64x+81`

Subtract
`81` on both sides:

`49-81=64x`

Simplify:

`-32=64x`

Divide both sides by 64:

`(-32)/(64)=x`

Reduce the fraction by dividing top and bottom by
`32`:

`(-1)/(2)=x`

The solution is -1/2.

Let's check it.

`|2((-1)/(2))-7|=|2((-1)/(2))+9|`

`|-1-7|=|-1+9|`

`|-8|=|8|`

`8=8`

So x=-1/2 does check out.

Another way: This is for all the people who hate quadratics.

We could consider cases. These cases must be checked.

`|2x-7|=|2x+9|` is
`2x-7=\pm (2x+9)`

Let's solve all four of these and then check the solutions.

2x-7=2x+9

Subtract 2x on both sides:

-7=9 (not possible)

Moving on.

2x-7=-(2x+9)

Distribute:

2x-7=-2x-9

Add 2x on both sides:

4x-7=-9

Add 7 on both sides

4x=-2

Divide both sides by 4:

x=-2/4

Simplify:

x=-1/2

We already checked this from before.