Question

solve each equation.
|3x + 9| = 30
x = 7
x = 1, - 19
no solution
x = 7, - 13
done
|2x + 1|=-13
no solution
x=-7
x=-14, 12
x=-7, 6
done
|x + 2|+4 = 11
x = 5
no solution
x = 5, - 9
x = 7, - 11
done

Explanation:

Step1: Solve $|3x + 9|=30$

Set up two equations: $3x+9 = 30$ and $3x + 9=-30$.
For $3x+9 = 30$, subtract 9 from both sides: $3x=30 - 9=21$, then divide by 3, $x = 7$.
For $3x + 9=-30$, subtract 9 from both sides: $3x=-30 - 9=-39$, then divide by 3, $x=-13$.

Step2: Solve $|2x + 1|=-13$

The absolute - value of a number is always non - negative. Since the right - hand side is negative, there is no solution.

Step3: Solve $|x + 2|+4 = 11$

First, subtract 4 from both sides: $|x + 2|=11 - 4 = 7$.
Set up two equations: $x + 2=7$ and $x + 2=-7$.
For $x + 2=7$, subtract 2 from both sides, $x = 5$.
For $x + 2=-7$, subtract 2 from both sides, $x=-9$.

Answer:

$|3x + 9| = 30$: $x = 7,-13$
$|2x + 1|=-13$: no solution
$|x + 2|+4 = 11$: $x = 5,-9$