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Solve for x in the following equations: a) 6x = 72, b) 7x = 84. Solve for x in the following equations: a) 5x − 6 = 18, b) 3x + 4 = -5. Substitute the given values into the equations: a) y = p2 + 7; p

Mathematics

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Here are the solutions to the problems from the image.

7. Solve for xx.

a) 6x=726x = 72

  1. Divide both sides by 6.

    6x6=726\frac{6x}{6} = \frac{72}{6}
  2. Simplify the equation.

    x=12x = 12

    The solution is x=12\boxed{x = 12}.

    b) 7x=847x = 84

  3. Divide both sides by 7.

    7x7=847\frac{7x}{7} = \frac{84}{7}
  4. Simplify the equation.

    x=12x = 12

    The solution is x=12\boxed{x = 12}.

    8. Solve for xx.

    a) 5x−6=185x - 6 = 18

  5. Add 6 to both sides of the equation.

    5x−6+6=18+65x - 6 + 6 = 18 + 6 5x=245x = 24
  6. Divide both sides by 5.

    5x5=245\frac{5x}{5} = \frac{24}{5}
  7. Simplify the equation.

    x=245orx=445x = \frac{24}{5} \quad \text{or} \quad x = 4\frac{4}{5}

    The solution is x=245\boxed{x = \frac{24}{5}}.

    b) 3x+4=−53x + 4 = -5

  8. Subtract 4 from both sides of the equation.

    3x+4−4=−5−43x + 4 - 4 = -5 - 4 3x=−93x = -9
  9. Divide both sides by 3.

    3x3=−93\frac{3x}{3} = \frac{-9}{3}
  10. Simplify the equation.

    x=−3x = -3

    The solution is x=−3\boxed{x = -3}.

    9. Substitute.

    a) y=p2+7y = p^2 + 7; p=8p = 8

  11. Substitute the value of pp into the equation.

    y=(8)2+7y = (8)^2 + 7
  12. Calculate the square.

    y=64+7y = 64 + 7
  13. Add the numbers.

    y=71y = 71

    The value of yy is y=71\boxed{y = 71}.

    b) y=c2+4y = c^2 + 4; c=5c = 5 (assuming c=5c=5 from the visible part of the question)

  14. Substitute the value of cc into the equation.

    y=(5)2+4y = (5)^2 + 4
  15. Calculate the square.

    y=25+4y = 25 + 4
  16. Add the numbers.

    y=29y = 29

    The value of yy is y=29\boxed{y = 29}.

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