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Question

Difficulty: HardLinear Equations in One Variable

If the equation 34(8x−12)−56(6x−18)=−12(4x−8)\frac{3}{4}(8x - 12) - \frac{5}{6}(6x - 18) = -\frac{1}{2}(4x - 8) is true, what is the value of xx?

  1. A
    283\frac{28}{3}
  2. B
    −103-\frac{10}{3}
  3. −23-\frac{2}{3}Answer
  4. D
    23\frac{2}{3}

Answer

−23-\frac{2}{3}
The correct answer is found by distributing the coefficients across each set of parentheses, combining like terms on the left side to get x+6=−2x+4x + 6 = -2x + 4, adding 2x2x to both sides to get 3x+6=43x + 6 = 4, subtracting 66 from both sides to get 3x=−23x = -2, and finally dividing by 33 to obtain −23-\frac{2}{3}.

Step-by-Step Solution

1
Distribute the coefficients to the terms inside the parentheses on both sides of the equation.
6x−9−5x+15=−2x+46x - 9 - 5x + 15 = -2x + 4
To eliminate the parentheses and prepare the equation for combining like terms.
2
Combine the constant and variable terms on the left side of the equation.
x+6=−2x+4x + 6 = -2x + 4
To simplify the left side of the equation.
3
Add 2x2x to both sides of the equation.
3x+6=43x + 6 = 4
To group all terms containing the variable xx on the left side.
4
Subtract 66 from both sides, then divide by 33 to solve for xx.
3x=−23x = -2, which gives x=−23x = -\frac{2}{3}
To isolate xx and find its value.

Key Concept

Linear Equations in One Variable
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Topics

Linear Equations in One Variable

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