Absolute value equations practice

Factor: $|3(x - 3)| = 24$, so $|x - 3| = 8$. The values of $x - 3$ are $8$ and $-8$; the positive value is $8$.

Rewrite $|5x + 10| = |5(x + 2)| = 35$, so $|x + 2| = 7$. The expression $x + 2$ equals $7$ or $-7$; the positive value is $7$.

Either $x - 7 = 15$, giving $x = 22$, or $x - 7 = -15$, giving $x = -8$. The positive value of $x$ is $22$.

Rewrite $|2x - 8| = |2(x - 4)| = 18$, so $|x - 4| = 9$. The expression $x - 4$ equals $9$ or $-9$; the positive value is $9$.

Rewrite $|6x + 12| = |6(x + 2)| = 48$, so $|x + 2| = 8$. The expression $x + 2$ equals $8$ or $-8$; the positive value is $8$.

The expression inside the absolute value is exactly $x + 5$, so $x + 5 = 13$ or $x + 5 = -13$. The positive value is $13$.

Rewrite $|4x + 16| = |4(x + 4)| = 52$, so $|x + 4| = 13$. The expression $x + 4$ equals $13$ or $-13$; the positive value is $13$.

Either $x - 2 = 11$, giving $x = 13$ and $2x = 26$, or $x - 2 = -11$, giving $x = -9$ and $2x = -18$. The positive value of $2x$ is $26$.