Practice Solving Multistep Equations with Distribution

1. Solve for $$p$$.
   

   $$10p-3 = 2(12+4p) -7$$

2. Solve for $$g$$.
   

   $$9g = 3(-4+5g) $$

3. Solve for $$e$$.
   

   $$7(2e-1) - 3 = 6+6e $$

4. Solve for $$m$$.
   $$m=-(4+m)+2 $$

Source: Khan Academy, https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:solve-equations-inequalities/x2f8bb11595b61c86:linear-equations-parentheses/e/multistep_equations_with_distribution
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1. We need to manipulate the equation to get \(p\) by itself.

   $$10 p-3  = 2(12+4 p)-7$$
   $$10 p-3  = 24+8 p-7 $$	Distribute
   $$10 p-3  = 17+8p$$	Combine like terms
   $$10 p-3-8 p = 17+8 p-8p $$	Subtract $$8p$$ from each side
   $$2 p-3  = 17$$	Combine like terms
   $$2 p-3+3  = 17+3$$	Add 3 to each side
   $$2 p  = 20 $$	Combine like terms
   $$\frac{2 p}{2}  = \frac{20}{2}$$	Divide each side by 2
   $$p  = 10$$	Simplify

   The answer:

   \(p=10\)

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

   $$9g  = 3(-4+5g) $$
   $$9g = -12+15g  $$	Distribute
   $$9g-15g  = -12+15g-15g   $$	Subtract $$15g$$ from each side
   $$-6g  = -12 $$	Combine like terms
   $$\frac{-6g}{-6} = \frac{-12}{-6} $$	Divide each side by -6
   $$g = 2 $$	Simplify

   
   

   The answer:

   \(g=2\)

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

   $$7(2e-1) - 3 = 6+6e $$
   $$14e-7 - 3 = 6+6e $$	Distribute
   $$14e-10 = 6+6e $$	Combine like terms
   $$14e-10-6e = 6+6e -6e$$	Subtract $$6e$$ from each side
   $$8e-10 = 6$$	Combine like terms
   $$8e-10+10 = 6+10$$	Add 10 to each side
   $$8e = 16$$	Combine like terms
   $$\frac{8e}{8} = \frac{16}{8}$$	Divide each side by 8
   $$e=2$$	Simplify

   The answer:

   \(e=2\)

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

   $$m=-(4+m)+2 $$
   $$m=-4-m+2 $$	Distribute
   $$m=-2-m $$	Combine like terms
   $$m+m=-2-m+m $$	Add $$m$$ to each side
   $$2m=-2 $$	Combine like terms
   $$\frac{2m}{2} = \frac{-2}{2}$$	Divide each side by 2
   $$m=-1$$	Simplify

   
   The answer:
   
   $$m=-1$$