Answer
$x = 1$
Work Step by Step
We need to solve each equation first.
Let's look at the first equation.
To get rid of the absolute value sign, we use the definition of absolute value to rewrite the equation as two equations, which is $|a|=b\implies a=b \quad \text{or} \quad a=-b$:
$x - 3 = -2$ or $x - 3 = 2$
Add $3$ to each side of the equation:
$x = 1$ or $x = 5$
Let's look at the second equation.
To get rid of the absolute value sign, we use the definition of absolute value to rewrite the equation as two equations:
$9 - x = -8$ or $9 - x = 8$
Subtract $9$ from each side of the equation:
$-x = -17$ or $-x = -1$
Divide both sides of the equation by $-1$:
$x = 17$ or $x = 1$
We want to find the common solution, which is $x = 1$.
