the absolute value of anything is a positive number so
lx-11l= 5x+10
x+11=5x+10
-x -x
11=4x+10
-10 -10
1=4x.
1/4=4x/4
1/4=x
1 divided by four = .25
so x =.25
With absolute value equations, we have:
[tex] |x| = \left\{ \begin{array}{ll} -x & \quad x \leq 0 \\ x & \quad x > 0 \end{array} \right. [/tex]
So, if x-11 is less than 0, we have -x+11, and if x-11 is greater than 0, we have x-11. Solving these two cases:
[tex] -x+11=5x+10 \implies \\-6x=-1\implies \\x=\frac{1}{6}\\\\x-11=5x+10 \implies \\-4x=-1 \implies \\x=\frac{1}{4} [/tex]
So, our two solutions are 1/6 and .25, and all absolute value equations are solved like this.
