So firstly, we need to isolate the absolute value onto one side. To do this, we must first add both sides by 2:
[tex]7|\frac{1}{2}x+3 \frac{1}{2}|=7[/tex]
Next, divide both sides by 7:
[tex]|\frac{1}{2}x+3 \frac{1}{2}|=1[/tex]
Now, we can split this equation to 2 equations: [tex]\frac{1}{2}x+3 \frac{1}{2}=1\ \textsf{and}\ \frac{1}{2}x+3 \frac{1}{2}=-1[/tex]
Let's start with the first equation. Firstly, subtract both sides by 3 1/2:
[tex]\frac{1}{2}x=-2\frac{1}{2}\\\\\frac{1}{2}x=-\frac{5}{2}[/tex]
Lastly, multiply both sides by 2 and your first answer will be [tex]x=-5[/tex]
Now, to the second equation. Firstly, subtract both sides by 3 1/2:
[tex]\frac{1}{2}x=-4\frac{1}{2}\\\\\frac{1}{2}x=-\frac{9}{2}[/tex]
Lastly, multiply both sides by 2 and your second answer will be [tex]x=-9[/tex]
