Question

[Tig27]

|2x-5|=7

2x-5=7
+5++5=12

2x=12
2 2

X=2

I got that, so the second part will be |2x-5|=-7

2x-5=-7
+5 +5

2x=-2

x=-1.

so the answer will be 2,-1... Is this correct?

 

[pka]

|2x-5|=7

Trying to solve this without understanding this basics is nuts.
\(\displaystyle |x|=a\ge 0\) stands for numbers that are a units from \(\displaystyle 0\).

So \(\displaystyle |2x-5|=7\) means the number \(\displaystyle (2x-5)\) is \(\displaystyle 7\) units from \(\displaystyle 0\).

Therefore \(\displaystyle 2x-5=7\text{ or }2x-5=-7~.\)

 

[lookagain]

I got that, so the second part will be |2x-5|=-7 That is not correct.

2x-5=-7
+5 +5

2x=-2

x=-1.

.
.
.

This absolute value equation, |2x - 5| = 7, splits into two non-absolute value equations:


\(\displaystyle 2x - 5 = 7 \ \ \ and \ \ \ 2x - 5 = -7.\)




(You drop the absolute value bars when you split up the
absolute value equation.)