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.
[tex](2x-7)^2=(2x+9)^2[/tex]
Expand both sides using: [tex](a+b)^2=a^2+2ab+b^2[/tex].
[tex]4x^2-28x+49=4x^2+36x+81[/tex]
Subtract [tex]4x^2[/tex] on both sides:
[tex]-28x+49=36x+81[/tex]
Add [tex]28x[/tex] on both sides:
[tex]49=64x+81[/tex]
Subtract [tex]81[/tex] on both sides:
[tex]49-81=64x[/tex]
Simplify:
[tex]-32=64x[/tex]
Divide both sides by 64:
[tex]\frac{-32}{64}=x[/tex]
Reduce the fraction by dividing top and bottom by [tex]32[/tex]:
[tex]\frac{-1}{2}=x[/tex]
The solution is -1/2.
Let's check it.
[tex]|2(\frac{-1}{2})-7|=|2(\frac{-1}{2})+9|[/tex]
[tex]|-1-7|=|-1+9|[/tex]
[tex]|-8|=|8|[/tex]
[tex]8=8[/tex]
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.
[tex]|2x-7|=|2x+9|[/tex] is [tex]2x-7=\pm (2x+9)[/tex]
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.
