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5x - 2/3 (7x − 4) = 3 − 3/2x

Mathematics

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Answer

−3435-\frac{34}{35}

Step-by-step solution

5 steps

  1. Distribute the fraction on the left side of the equation.

    5x−23(x−4)=−3−32x5x - \frac{2}{3}(x-4) = -3 - \frac{3}{2}x 5x−23x+23×4=−3−32x5x - \frac{2}{3}x + \frac{2}{3} \times 4 = -3 - \frac{3}{2}x 5x−23x+83=−3−32x5x - \frac{2}{3}x + \frac{8}{3} = -3 - \frac{3}{2}x

  2. Clear the denominators by multiplying the entire equation by the least common multiple (LCM) of 3 and 2, which is 6.

    6(5x−23x+83)=6(−3−32x)6 \left( 5x - \frac{2}{3}x + \frac{8}{3} \right) = 6 \left( -3 - \frac{3}{2}x \right) 6(5x)−6(23x)+6(83)=6(−3)−6(32x)6(5x) - 6\left(\frac{2}{3}x\right) + 6\left(\frac{8}{3}\right) = 6(-3) - 6\left(\frac{3}{2}x\right) 30x−4x+16=−18−9x30x - 4x + 16 = -18 - 9x

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

    (30−4)x+16=−18−9x(30-4)x + 16 = -18 - 9x 26x+16=−18−9x26x + 16 = -18 - 9x

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

    Add 9x9x to both sides:

    26x+9x+16=−1826x + 9x + 16 = -18 35x+16=−1835x + 16 = -18

    Subtract 16 from both sides:

    35x=−18−1635x = -18 - 16 35x=−3435x = -34

  5. Solve for xx.

    x=−3435x = -\frac{34}{35}

    The final answer is −3435-\frac{34}{35}.

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