### Home > A2C > Chapter 5 > Lesson 5.1.2 > Problem5-29

5-29.

Solve each of the following equations for the indicated variable.

1. $5x − 3y = 12$ for $y$

Remember the strategies for solving algebraically.

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

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

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

To undo division by r2, multiply both sides by r2.

To undo multiplication by Gm1 divide both sides by Gm1.

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

$\text{To undo multiplication by } \frac{1}{2}$

(which is the same as dividing by 2), multiply both sides by 2.

To undo multiplication by v2, divide both sides by v2.

4. (x − 4)2 + (y − 1)2 = 10 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 ±.)

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

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