Practice Problems

Answers

  1. We need to manipulate the equation to get ‍c by itself.

    0.2(10-5c) = 5c-16
    2-c = 5c-16
    		Distribute
    2-c {-5c} = 5c-16 {-5c}
    		Subtract 5c from each side
    2-6c = -16
    		Combine like terms
    2-6c {-2} = -16 {-2}
    		Subtract 2 from each side
    -6c =-18
    		Combine like terms
    \dfrac{-6c}{ {-6}} = \dfrac{-18}{ {-6}}
    		Divide each side by -6
    c = {3}
    		Simplify

    The answer: c = { 3 }

  2. We need to manipulate the equation to get ‍e by itself.

    0.75(8+e)=2-1.25e
    6+0.75e=2-1.25e
    		Distribute
    6+0.75e{+1.25e} = 2-1.25e{+1.25e}
    		Add 1.25e to each side
    6+2e =2
    		Combine like terms
    6+2e -6 =2 -6
    		Subtract 6 from each side
    2e = -4
    		Combine like terms
    \dfrac{2e}{{2}} = \dfrac{-4}{{2}}
    		Divide each side by 2
    e = {-2}
    		Simplify


    The answer: e = {-2}

  3. We need to manipulate the equation to get ‍m by itself.

    4(1+0.5m)=7m
    4+2m = 7m
    		Distribute
    4+2m{-2m} = 7m{-2m}
    		Subtract 2m from each side
    4 =5m
    		Combine like terms
    2-6c {-2} = -16 {-2}
    		Subtract 2 from each side
    -6c =-18
    		Combine like terms
    \dfrac{4}{{5}} = \dfrac{5m}{{5}}
    		Divide each side by 5
    m = {0.8}
    		Simplify


    The answer: m = {0.8}

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

    0.5(7d+4)=7-1.5d
    3.5d+2 = 7-1.5d
    		Distribute
    3.5d+2{+1.5d} = 7-1.5d{+1.5d}
    		Add 1.5d to each side
    5d =5
    		Combine like terms
    5d+2{-2} = 7{-2}
    		Subtract 2 from each side
    2e = -4
    		Combine like terms
    \dfrac{5d}{{5}} = \dfrac{5}{{5}}
    		Divide each side by 5
    d = {1}
    		Simplify


    The answer: d = {1}

Back to '1.1: Solving Linear and Rational Equations in One Variable'