HSA.REI.B.3 math practice. Learn by doing.

The equation means $x + 8 = 21$ or $x + 8 = -21$. So $x = 13$ or $x = -29$. Both solutions are $-29$ and $13\textsf{.}$

Factor: $|3x - 9| = |3(x - 3)| = |3|\,|x - 3| = 3|x - 3|$. Since $3|x - 3| = 24$, divide by $3$ to get $|x - 3| = 8$. The values of $x - 3$ are $8$ and $-8$; the negative value is $-8\textsf{.}$

Subtract $6$ from both sides: $3x = 18$, so $x = 6$. Then $2x = 2 \cdot 6 = 12\textsf{.}$

Divide both sides by $-2$ and flip the inequality: $x < -3$. The greatest integer less than $-3$ is $-4$.

Substitute $a = 4$: $5(4) + 3c = 41$, so $20 + 3c = 41$. Then $3c = 21$ and $c = 7$.

The equation means $x - 25 = 40$ or $x - 25 = -40$. So $x = 65$ or $x = -15$. Both solutions are $-15$ and $65\textsf{.}$

Rewrite $|5x + 10| = |5(x + 2)| = |5|\,|x + 2| = 5|x + 2|$. Since $5|x + 2| = 35$, divide by $5$ to get $|x + 2| = 7$. The expression $x + 2$ equals $7$ or $-7$; the positive value is $7\textsf{.}$

Subtract $6$ from both sides: $2x = 20$, so $x = 10$. Then $15 - x = 15 - 10 = 5\textsf{.}$