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Practice Solving Multistep Equations with Distribution

Practice Problems

Answers

  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:

    \(p=10\)

  1. 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:

    \(g=2\)

  1. 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:

    \(e=2\)

  1. 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:

    $$m=-1$$