Answer
x=2
Work Step by Step
We are given that $|x+3|=|7−x|$
So $x+3=7−x$ or $x+3=−(7−x)$
We can solve both of these equations for x.
For $x+3=7−x$, subtract 3 from both sides of the equation.
$x=4−x$
Add x to both sides of the equation.
$2x=4$
Divide both sides of the equation by 2.
$x=2$
For $x+3=-(7−x)$, use the distributive property to simplify the right side of the equation.
$x+3=x-7$
Subtract x from both sides of the equation.
$3=−7$
This is false, so the only solution is x=2.