Solve each of the following equations for the indicated variable.

1. $5x − 3y = 12$ for $y$

   Hint (a):

   Remember the strategies for solving algebraically.

   More Help (a):

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

   Answer (a):

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

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

   Hint (b):

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

   More Help (b):

   To undo multiplication by Gm₁ divide both sides by Gm₁.

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

   Hint (c):

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

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

   More Help (c):

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

4. (x − 4)² + (y − 1)² = 10 for y

   Hint (d):

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

   Hint 2(d):

   To undo squaring, take the square root of both sides. (Remember ±.)

   More Help (d):

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

   Answer (d):

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