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Solve the following equations: a) x2 − 1 = 0 b) 2x − 4 = 0 c) x − 7 = 0 d) 3x + 6 = 0

Mathematics

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Step-by-step solution

7 steps

Here are the solutions for each equation:

Equation 1:
We need to solve the equation x2−1=0x^2 - 1 = 0.

  1. Add 1 to both sides of the equation.

    x2=1x^2 = 1
  2. Take the square root of both sides.

    Remember to consider both positive and negative roots.

    x=±1x = \pm \sqrt{1} x=±1x = \pm 1

    The solutions are x=1x = 1 and x=−1x = -1.

    x=1,−1\boxed{x = 1, -1}

    Equation 2:
    We need to solve the equation 2x−4=02x - 4 = 0.

  3. Add 4 to both sides of the equation.

    2x=42x = 4
  4. Divide both sides by 2.

    x=42x = \frac{4}{2} x=2x = 2

    The solution is x=2x = 2.

    x=2\boxed{x = 2}

    Equation 3:
    We need to solve the equation x−7=0x - 7 = 0.

  5. Add 7 to both sides of the equation.

    x=7x = 7

    The solution is x=7x = 7.

    x=7\boxed{x = 7}

    Equation 4:
    We need to solve the equation 3x+6=03x + 6 = 0.

  6. Subtract 6 from both sides of the equation.

    3x=−63x = -6
  7. Divide both sides by 3.

    x=−63x = \frac{-6}{3} x=−2x = -2

    The solution is x=−2x = -2.

    x=−2\boxed{x = -2}
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