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Practice Solving Equations with Variables on Both Sides

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:

    $$d=-2$$