Question

|x-11|= 5x +10 how do I solve this

Answer 1

With absolute value equations, we have:

$|x| = \left\{ \begin{array}{ll} -x & \quad x \leq 0 \\ x & \quad x > 0 \end{array} \right.$

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:

$-x+11=5x+10 \implies \\-6x=-1\implies \\x=\frac{1}{6}\\\\x-11=5x+10 \implies \\-4x=-1 \implies \\x=\frac{1}{4}$

So, our two solutions are 1/6 and .25, and all absolute value equations are solved like this.

Answer 2

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