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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:

    \(m=-1\)