### Home > CCA2 > Chapter Ch4 > Lesson 4.1.2 > Problem4-32

4-32.

Solve each of the following equations for the indicated variable.

1. $5 x - 3 y = 12 \text { for } y$

Remember the strategies for solving algebraically.

To undo multiplication by $3$, divide each term by $3$.

$\textit{y}=\frac{5}{3}\textit{x}-4$

1. $F = \frac { G m _ { 1 } m _ { 2 } } { r ^ { 2 } } \text { for } m _ { 2 }$

To undo division by $r^2$, multiply both sides by $r^2$.

To undo multiplication by $Gm_1$ divide both sides by $Gm_1$.

1. $E = \frac { 1 } { 2 } m v ^ { 2 } \text { for } m$

To undo multiplication by $\frac{1}{2}$, multiply both sides by $2$.

To undo multiplication by $v^2$, divide both sides by $v^2$.

1. $( x - 4 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 10 \text { for } y$

To undo addition of $(x−4)^2$, subtract $(x−4)^2$ from both sides.

To undo squaring, take the square root of both sides. (Remember $\pm$.)

To undo subtracting $1$, add $1$ to both sides. Remember to put it outside the radical sign.

$\textit{y}=\pm\sqrt{10-(\textit{x}-4)^{2}}+1$