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Solve for x: a) x − 4 = 9 b) 2x − 15 = 1 c) x2 − 8x = 0

Mathematics

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Answers

3 parts
a

x=13x=13

b

x=8x=8

c

x=0 or x=8x=0 \text{ or } x=8

Step-by-step solution

6 steps

Here are the solutions for the homework problems:

Part a· 1 step

  1. Add 4 to both sides of the equation.

    x−4=9x-4=9 x=9+4x = 9+4 x=13x = 13

    The student's answer is correct.

    x=13\boxed{x=13}

Part b

x=8x=8

  1. Add 15 to both sides of the equation.

    2x−15=12x-15=1 2x=1+152x = 1+15 2x=162x = 16

  2. Divide both sides by 2.

    2x2=162\frac{2x}{2} = \frac{16}{2} x=8x = 8 x=8\boxed{x=8}

Part c

x=0 or x=8x=0 \text{ or } x=8

  1. Factor out the common term xx from the equation.

    x2−8x=0x^2-8x=0 x(x−8)=0x(x-8)=0

  2. Set each factor equal to zero to find the possible values for xx.

    x=0orx−8=0x=0 \quad \text{or} \quad x-8=0

  3. Solve the second equation for xx.

    x−8=0x-8=0 x=8x=8 x=0 or x=8\boxed{x=0 \text{ or } x=8}
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