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When a number is double and 8 added to it, the result is the same as multiplying the number by 3 and subtracting 7 from it. Find the number.

Mathematics

ScanSolve AI Answer

Answer

15

Step-by-step solution

5 steps

  1. Define the unknown number.

    Let the number be xx.

  2. Translate the first part of the statement into an algebraic expression.

    "when it is double and 8 added to it" means 2x+82x + 8.

  3. Translate the second part of the statement into an algebraic expression.

    "multiplying the number by 3 and subtracting 7 from the number" means 3x−73x - 7.

  4. Formulate the equation by equating the two expressions.

    The problem states that the results from Step 2 and Step 3 are the same.

    2x+8=3x−72x + 8 = 3x - 7

  5. Solve the equation for xx.

    Subtract 2x2x from both sides:

    8=3x−2x−78 = 3x - 2x - 7 8=x−78 = x - 7

    Add 7 to both sides:

    8+7=x8 + 7 = x x=15x = 15

    The equation is 2x+8=3x−72x + 8 = 3x - 7.
    The number is 15.

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