Examkin

Question

Difficulty: MediumLinear Equations in One Variable

If 2(3x−4)−5(x−1)=3(x+2)−12(3x - 4) - 5(x - 1) = 3(x + 2) - 1, what is the value of 2x+32x + 3?

  1. A
    -15
  2. -5Answer
  3. C
    5
  4. D
    11

Answer

The correct answer is −5-5.
Solving the given equation step-by-step yields x=−4x = -4. Substituting x=−4x = -4 into the expression 2x+32x + 3 results in 2(−4)+3=−52(-4) + 3 = -5.

Step-by-Step Solution

1
Distribute the values outside the parentheses on both sides of the equation.
6x−8−5x+5=3x+6−16x - 8 - 5x + 5 = 3x + 6 - 1
This step removes parentheses so that like terms can be combined.
2
Combine like terms on each side of the equation.
x−3=3x+5x - 3 = 3x + 5
Simplifying both sides makes it easier to isolate the variable.
3
Isolate the variable xx by subtracting xx and 55 from both sides.
x=−4x = -4
This determines the value of xx which is required to evaluate the final expression.
4
Substitute the value of xx into the expression 2x+32x + 3.
2(−4)+3=−52(-4) + 3 = -5
This calculates the final value requested by the question.

Key Concept

Solving linear equations in one variable involving parentheses and distributing terms.
Rate this question

Topics

Linear Equations in One Variable

More questions from this topic