Practice Solving Equations with Variables on Both Sides

1. Solve for $$h$$
   

   $$17+4h+2=1-5h$$

2. Solve for $$c$$
   

   $$12c−4=14c−10$$

3. Solve for $$r$$
   

   $$16−2r=-3r+6r+1$$

4. Solve for $$d$$
   $$2d+ 4=10+5d$$

Source: Khan Academy, https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:linear-equations-variables-both-sides/e/linear_equations_3
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.

1. We need to manipulate the equation to get \(h\) by itself.

   $$17+4h+2=1-5h$$
   $$19+4h=1-5h$$	Combine like terms
   $$19+4h+5h=1-5h+5h$$	Add $$5h$$ to each side
   $$9h+19=1$$	Combine like terms
   $$9h+19-19=1-19$$	Subtract 19 from each side
   $$9h=-18$$	Combine like terms
   $$\frac{9h}{9}  = \frac{-18}{9}$$	Divide each side by 9
   $$h  = -2$$	Simplify

   
   The answer:

   \(h=-2\)

2. We need to manipulate the equation to get \(c\) by itself.

   $$12c−4=14c−10$$
   $$12c−4-14c=14c−10-14c$$	Subtract $$14c$$ from each side
   $$-2c−4=−10$$	Combine like terms
   $$-2c−4+4=−10+4$$	Add 4 to each side
   $$-2c=−6$$	Combine like terms
   $$\frac{-2c}{-2} = \frac{-6}{-2} $$	Divide each side by -2
   $$c = 3 $$	Simplify

   
   

   The answer:

   \(c=3\)

3. We need to manipulate the equation to get \(r\) by itself.

   $$16−2r=-3r+6r+1$$
   $$16−2r=3r+1$$	Combine like terms
   $$16−2r-3r=3r+1-3r$$	Subtract $$3r$$ from each side
   $$16−5r=1$$	Combine like terms
   $$16−5r-16=1-16$$	Subtract 16 from each side
   $$−5r=-15$$	Combine like terms
   $$\frac{-5r}{-5} = \frac{-15}{-5}$$	Divide each side by -5
   $$r=3$$	Simplify

   
   The answer:

   \(r=3\)

4. We need to manipulate the equation to get \(d\) by itself.

   $$2d+ 4=10+5d$$
   $$2d+ 4-5d=10+5d-5d$$	Subtract $$5d$$ from each side
   $$-3d+4=10$$	Combine like terms
   $$-3d+4-4=10-4$$	Subtract 4 from each side
   $$-3d=6$$	Combine like terms
   $$\frac{-3d}{-3} = \frac{6}{-3}$$	Divide each side by -3
   $$d=-2$$	Simplify

   
   The answer:
   
   $$d=-2$$