2x−1 ÷3 − 3 −x÷2 = x÷ 4

Mathematics

ScanSolve AI Answer

Step-by-step solution

6 steps

  1. Write the equation.

    2x−13−3−x2=x4\frac{2x-1}{3} - 3 - \frac{x}{2} = \frac{x}{4}

  2. Find a common denominator for all terms.

    The least common multiple of 3, 2, and 4 is 12. Multiply every term by 12.

    12(2x−13)−12(3)−12(x2)=12(x4)12 \left( \frac{2x-1}{3} \right) - 12(3) - 12 \left( \frac{x}{2} \right) = 12 \left( \frac{x}{4} \right)

  3. Simplify the equation.

    4(2x−1)−36−6x=3x4(2x-1) - 36 - 6x = 3x

  4. Distribute and combine like terms on the left side.

    8x−4−36−6x=3x8x - 4 - 36 - 6x = 3x (8x−6x)+(−4−36)=3x(8x - 6x) + (-4 - 36) = 3x 2x−40=3x2x - 40 = 3x

  5. Isolate the variable x by subtracting 2x from both sides.

    −40=3x−2x-40 = 3x - 2x −40=x-40 = x

  6. State the final answer.

    x=−40x = -40

    The solution is x = -40.

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