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Question

Difficulty: MediumLinear Equations in One Variable

If 34(8x−12)−12(2x−6)=18\frac{3}{4}(8x - 12) - \frac{1}{2}(2x - 6) = 18, what is the value of 5x5x?

  1. 24Answer
  2. B
    30
  3. C
    12
  4. D
    27

Answer

24
By distributing the fractions to the terms inside the parentheses, we get 6x−9−x+3=186x - 9 - x + 3 = 18. Combining like terms on the left side yields 5x−6=185x - 6 = 18. Adding 6 to both sides gives the value of 5x5x as 24.

Step-by-Step Solution

1
Distribute the coefficients outside the parentheses to the terms inside.
34(8x)−34(12)−12(2x)+12(6)=18\frac{3}{4}(8x) - \frac{3}{4}(12) - \frac{1}{2}(2x) + \frac{1}{2}(6) = 18, which simplifies to 6x−9−x+3=186x - 9 - x + 3 = 18.
To eliminate the parentheses and prepare to combine like terms.
2
Combine like terms on the left side of the equation.
(6x−x)+(−9+3)=18(6x - x) + (-9 + 3) = 18, which simplifies to 5x−6=185x - 6 = 18.
To simplify the linear expression on the left side.
3
Isolate the term 5x5x by adding 6 to both sides of the equation.
5x=18+65x = 18 + 6, which simplifies to 5x=245x = 24.
To find the value of 5x5x directly as requested by the question.

Key Concept

Solving linear equations in one variable using the distributive property and combining like terms.
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Topics

Linear Equations in One Variable

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