# Absolute Value (with extra terms)

Find the value of $x$ in the absolute value equations:

1.

\eqalign{|x|+2&=8\\|x|&=6 \\\mathbf{x=6} \qquad & \qquad \mathbf{x=-6}}

2.

\eqalign{|x|-7&=9\\|x|&=16\\\mathbf{x=16} \qquad & \qquad \mathbf{x=-16}}

3.

\eqalign{2|x|+6&=2\\2|x|&=16\\|x|&=8\\\mathbf{x=8} \qquad & \qquad \mathbf{x=8}}

4.

\eqalign{|x+7|+1&=10\\|x+7|&=9\\x+7=9 \qquad & \qquad x+7=-9\\\mathbf{x=2} \qquad & \qquad \mathbf{x=-16}}

5.

\eqalign{|x-2|-9&=-1\\|x-2|&=8\\x-2=8 \qquad & \qquad x-2=-8\\\mathbf{x=10} \qquad & \qquad \mathbf{x=-6}}

6.

\eqalign{3|x-1|+1&=4\\3|x-1|&=3\\|x-1|&=1\\x-1=1 \qquad & \qquad x-1=-1\\\mathbf{x=2} \qquad & \qquad \mathbf{x=0}}

7.

\eqalign{-2|x+7|-9&=-5\\-2|x+7|&=4\\|x-1|&=-2\\\mathbf{\text{No real solution}}}

8.

\eqalign{-|3x|+2&=12\\-|3x|&=10\\|3x|&=-10\\\mathbf{\text{No real solution}}}

9.

\eqalign{-4|2x-11|+20&=10\\-4|2x-11|&=-10\\|2x-11|&=2.5\\2x-11=2.5 \qquad & \qquad 2x-11=-2.5\\2x=13.5 \qquad & \qquad 2x=8.5\\\mathbf{x=6.75} \qquad & \qquad \mathbf{x=4.25}}

10.

\eqalign{3|2x|+19&=17\\3|2x|&=36\\|2x|&=12\\2x=12 \qquad & \qquad 2x=-12\\\mathbf{x=6} \qquad & \qquad \mathbf{x=-6}}

11.

\eqalign{-5|-2x+4|-8&=2\\-5|-2x+4|&=10\\|-2x+4|&=-2\\\mathbf{\text{No real solution}}}

12.

\eqalign{-|-9x-3|-2&=-8\\-|-9x-3|&=-6\\|-9x-3|&=6\\-9x-3=6 \qquad & \qquad -9x-3=-6\\-9x=9 \qquad & \qquad -9x=-3 \\\mathbf{x=-1} \qquad & \qquad \mathbf{x=\dfrac{1}{3}}}