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Question

Difficulty: MediumLinear Equations in One Variable

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

  1. −4-4Answer
  2. B
    83\frac{8}{3}
  3. C
    −5-5
  4. D
    −143-\frac{14}{3}

Answer

−4-4
The correct answer is −4-4. Distributing the terms on the left side of the equation 12(4x−6)−2(x+5)=3x−1\frac{1}{2}(4x - 6) - 2(x + 5) = 3x - 1 gives 2x−3−2x−10=3x−12x - 3 - 2x - 10 = 3x - 1. Simplifying the left side yields −13=3x−1-13 = 3x - 1. Adding 11 to both sides results in −12=3x-12 = 3x. Finally, dividing both sides by 33 gives x=−4x = -4.

Step-by-Step Solution

1
Distribute the constants outside the parentheses on the left side of the equation.
2x−3−2x−10=3x−12x - 3 - 2x - 10 = 3x - 1
Distributing 12\frac{1}{2} to (4x−6)(4x - 6) yields 2x−32x - 3, and distributing −2-2 to (x+5)(x + 5) yields −2x−10-2x - 10.
2
Combine like terms on the left side of the equation.
−13=3x−1-13 = 3x - 1
Combining 2x2x and −2x-2x results in 00, and combining −3-3 and −10-10 results in −13-13.
3
Isolate the variable xx by adding 11 to both sides and dividing by 33.
x=−4x = -4
Adding 11 to both sides gives −12=3x-12 = 3x. Dividing both sides by 33 yields x=−4x = -4.

Key Concept

Solving linear equations in one variable by distributing constants and combining like terms.
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Topics

Linear Equations in One Variable

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