Practice Problems

Answers

  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:

    \(h=-2\)

  1. 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:

    \(c=3\)

  1. 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:

    \(r=3\)

  1. 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:

    \(d=-2\)
Back to '2.5: Equations with Variables on Both Sides'