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Solve the following equations: 5 − b = 1; 3 = 7p; c/11 = 2; 5 = 10x; n + 3 = -4; 2x + 5 = 17

Mathematics

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  1. Identify the equation.

    5−b=15 - b = 1

  2. Subtract 5 from both sides of the equation.

    5−b−5=1−55 - b - 5 = 1 - 5 −b=−4-b = -4

  3. Multiply both sides by -1 to solve for bb.

    (−1)(−b)=(−1)(−4)(-1)(-b) = (-1)(-4) b=4b = 4

    The solution is:

    b=4\boxed{b = 4}

    :

  4. Identify the equation.

    3=7p3 = 7p

  5. Divide both sides by 7 to isolate pp.

    37=7p7\frac{3}{7} = \frac{7p}{7} 37=p\frac{3}{7} = p

    The solution is:

    p=37\boxed{p = \frac{3}{7}}

    :

  6. Identify the equation.

    c11=2\frac{c}{11} = 2

  7. Multiply both sides by 11 to isolate cc.

    c11×11=2×11\frac{c}{11} \times 11 = 2 \times 11 c=22c = 22

    The solution is:

    c=22\boxed{c = 22}

    :

  8. Identify the equation.

    5=10x5 = 10x

  9. Divide both sides by 10 to isolate xx.

    510=10x10\frac{5}{10} = \frac{10x}{10} 12=x\frac{1}{2} = x

    The solution is:

    x=12\boxed{x = \frac{1}{2}}

    :

  10. Identify the equation.

    n+3=−4n + 3 = -4

  11. Subtract 3 from both sides of the equation.

    n+3−3=−4−3n + 3 - 3 = -4 - 3 n=−7n = -7

    The solution is:

    n=−7\boxed{n = -7}

    :

  12. Identify the equation.

    2x+5=172x + 5 = 17

  13. Subtract 5 from both sides of the equation.

    2x+5−5=17−52x + 5 - 5 = 17 - 5 2x=122x = 12

  14. Divide both sides by 2 to isolate xx.

    2x2=122\frac{2x}{2} = \frac{12}{2} x=6x = 6

    The solution is:

    x=6\boxed{x = 6}

    :

  15. Identify the equation.

    3(x−4)=153(x - 4) = 15

  16. Divide both sides by 3.

    3(x−4)3=153\frac{3(x - 4)}{3} = \frac{15}{3} x−4=5x - 4 = 5

  17. Add 4 to both sides of the equation.

    x−4+4=5+4x - 4 + 4 = 5 + 4 x=9x = 9

    The solution is:

    x=9\boxed{x = 9}
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