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Solve the equation x+7-(8x)/(3) = (17)/(6) - (5x)/(2).

Mathematics

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Answer

-5

Step-by-step solution

6 steps

To solve the equation x+7−8x3=176−5x2x+7-\frac{8x}{3} = \frac{17}{6} - \frac{5x}{2}, we need to find a common denominator for all fractions.

  1. Identify the denominators.

    The denominators are 1 (for xx and 7), 3, 6, and 2. The least common multiple (LCM) of 1, 3, 6, and 2 is 6.

  2. Multiply every term in the equation by the LCM (6) to eliminate the denominators.

    6(x)+6(7)−6(8x3)=6(176)−6(5x2)6(x) + 6(7) - 6\left(\frac{8x}{3}\right) = 6\left(\frac{17}{6}\right) - 6\left(\frac{5x}{2}\right)

  3. Simplify each term.

    6x+42−(2×8x)=17−(3×5x)6x + 42 - (2 \times 8x) = 17 - (3 \times 5x) 6x+42−16x=17−15x6x + 42 - 16x = 17 - 15x

  4. Combine like terms on each side of the equation.

    On the left side: 6x−16x=−10x6x - 16x = -10x
    So, the equation becomes:

    −10x+42=17−15x-10x + 42 = 17 - 15x

  5. Move all terms containing xx to one side and all constant terms to the other side.

    Add 15x15x to both sides:

    −10x+15x+42=17-10x + 15x + 42 = 17 5x+42=175x + 42 = 17

    Subtract 42 from both sides:

    5x=17−425x = 17 - 42 5x=−255x = -25

  6. Solve for xx.

    Divide both sides by 5:

    x=−255x = \frac{-25}{5} x=−5x = -5

    The final answer is −5-5.

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