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Solve for the variables in the following equations: a) 15 + a = 28 b) b − 35 = 27 c) 3c = 69 d) d/8 = 12 e) 3e + 14 = 26 f) 2b − 10 = 40

Mathematics

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Answers

6 parts
a

13\text{13}

b

62\text{62}

c

23\text{23}

d

96\text{96}

e

4\text{4}

f

25\text{25}

Step-by-step solution

16 steps

Here are the solutions to the equations:

Part a· 2 steps

Solve for aa

  1. Subtract 15 from both sides of the equation.

    15+a−15=28−1515 + a - 15 = 28 - 15
  2. Simplify.

    a=13a = 13

    The value of aa is 13\boxed{\text{13}}.

Part b

62\text{62}

Solve for bb

  1. Add 35 to both sides of the equation.

    b−35+35=27+35b - 35 + 35 = 27 + 35
  2. Simplify.

    b=62b = 62

    The value of bb is 62\boxed{\text{62}}.

Part c

23\text{23}

Solve for cc

  1. Divide both sides of the equation by 3.

    3c3=693\frac{3c}{3} = \frac{69}{3}
  2. Simplify.

    c=23c = 23

    The value of cc is 23\boxed{\text{23}}.

Part d

96\text{96}

Solve for dd

  1. Multiply both sides of the equation by 8.

    d8×8=12×8\frac{d}{8} \times 8 = 12 \times 8
  2. Simplify.

    d=96d = 96

    The value of dd is 96\boxed{\text{96}}.

Part e

4\text{4}

Solve for ee

  1. Subtract 14 from both sides of the equation.

    3e+14−14=26−143e + 14 - 14 = 26 - 14
  2. Simplify.

    3e=123e = 12
  3. Divide both sides by 3.

    3e3=123\frac{3e}{3} = \frac{12}{3}
  4. Simplify.

    e=4e = 4

    The value of ee is 4\boxed{\text{4}}.

Part f

25\text{25}

Solve for bb

  1. Add 10 to both sides of the equation.

    2b−10+10=40+102b - 10 + 10 = 40 + 10
  2. Simplify.

    2b=502b = 50
  3. Divide both sides by 2.

    2b2=502\frac{2b}{2} = \frac{50}{2}
  4. Simplify.

    b=25b = 25

    The value of bb is 25\boxed{\text{25}}.

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