Examkin

Question

Difficulty: MediumLinear Equations in One Variable

If 3(x−2)−4(2−x)=12(6x−4)+13(x - 2) - 4(2 - x) = \frac{1}{2}(6x - 4) + 1, what is the value of 2x−32x - 3?

  1. A
    −192-\frac{19}{2}
  2. 72\frac{7}{2}Answer
  3. C
    92\frac{9}{2}
  4. D
    134\frac{13}{4}

Answer

The value of the expression is 72\frac{7}{2}.
The correct answer is 72\frac{7}{2}. Distributing the constants on both sides of the equation 3(x−2)−4(2−x)=12(6x−4)+13(x - 2) - 4(2 - x) = \frac{1}{2}(6x - 4) + 1 yields 3x−6−8+4x=3x−2+13x - 6 - 8 + 4x = 3x - 2 + 1. Combining like terms on both sides gives 7x−14=3x−17x - 14 = 3x - 1. Subtracting 3x3x from both sides and adding 1414 to both sides results in 4x=134x = 13, which simplifies to x=134x = \frac{13}{4}. Substituting this value into 2x−32x - 3 gives 2(134)−3=132−3=722\left(\frac{13}{4}\right) - 3 = \frac{13}{2} - 3 = \frac{7}{2}.

Step-by-Step Solution

1
Distribute the constants on both sides of the equation.
3x−6−8+4x=3x−2+13x - 6 - 8 + 4x = 3x - 2 + 1
To simplify the linear terms and constants before isolating the variable.
2
Combine like terms on both sides of the equation.
7x−14=3x−17x - 14 = 3x - 1
To reduce the equation to a simpler form with one variable term and one constant term on each side.
3
Isolate the variable term by subtracting 3x3x from both sides and adding 1414 to both sides.
4x=134x = 13
To group all variable terms on one side and constant terms on the other.
4
Solve for xx by dividing both sides by 44.
x=134x = \frac{13}{4}
To isolate the variable xx.
5
Substitute the value of xx into the expression 2x−32x - 3.
2(134)−3=132−3=722\left(\frac{13}{4}\right) - 3 = \frac{13}{2} - 3 = \frac{7}{2}
To calculate the final value requested by the question.

Key Concept

Solving linear equations in one variable by distributing terms, combining like terms, isolating the variable, and evaluating algebraic expressions.
Rate this question

Topics

Linear Equations in One Variable

More questions from this topic