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Solve for x: (4x-9)/(3) = (3x+5)/(7)

Mathematics

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Answer

x=7819x = \frac{78}{19}

Step-by-step solution

6 steps

  1. Write the given equation.

    4x−93=3x+57\frac{4x-9}{3} = \frac{3x+5}{7}

  2. Multiply both sides by the least common multiple of the denominators (3 and 7), which is 21, to eliminate the fractions.

    21⋅4x−93=21⋅3x+5721 \cdot \frac{4x-9}{3} = 21 \cdot \frac{3x+5}{7} 7(4x−9)=3(3x+5)7(4x-9) = 3(3x+5)

  3. Distribute the numbers on both sides of the equation.

    28x−63=9x+1528x - 63 = 9x + 15

  4. Subtract 9x9x from both sides to gather xx terms on one side.

    28x−9x−63=1528x - 9x - 63 = 15 19x−63=1519x - 63 = 15

  5. Add 63 to both sides to gather constant terms on the other side.

    19x=15+6319x = 15 + 63 19x=7819x = 78

  6. Divide both sides by 19 to solve for xx.

    x=7819x = \frac{78}{19}
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