Question

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

Answer 1

Answer:

-1/2

Step-by-step 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:

$\frac{-32}{64}=x$

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

$\frac{-1}{2}=x$

The solution is -1/2.

Let's check it.

$|2(\frac{-1}{2})-7|=|2(\frac{-1}{2})+9|$

$|-1-7|=|-1+9|$

$|-8|=|8|$

$8=8$

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.