Examkin

Question

Difficulty: MediumLinear Equations in One Variable

If 5−3(2x−4)=2(x+3)−55 - 3(2x - 4) = 2(x + 3) - 5, what is the value of 4x−34x - 3?

  1. 5Answer
  2. B
    -7
  3. C
    2
  4. D
    6

Answer

5
The correct answer is the value of the expression when the linear equation is solved correctly. Distributing the terms on both sides of the equation yields 5−6x+12=2x+6−55 - 6x + 12 = 2x + 6 - 5. Simplifying each side gives 17−6x=2x+117 - 6x = 2x + 1. Adding 6x6x to both sides and subtracting 11 from both sides results in 16=8x16 = 8x, which means x=2x = 2. Substituting x=2x = 2 into the expression 4x−34x - 3 gives 4(2)−3=54(2) - 3 = 5.

Step-by-Step Solution

1
Distribute the constants on both sides of the equation.
5−6x+12=2x+6−55 - 6x + 12 = 2x + 6 - 5
To eliminate the parentheses so that like terms can be combined.
2
Combine like terms on both sides of the equation.
17−6x=2x+117 - 6x = 2x + 1
To simplify the linear expression on each side.
3
Isolate the variable xx by adding 6x6x to both sides and subtracting 11 from both sides.
16=8x16 = 8x, which simplifies to x=2x = 2
To find the value of xx that satisfies the equation.
4
Substitute the value of xx into the target expression 4x−34x - 3.
4(2)−3=54(2) - 3 = 5
To find the final value requested by the question.

Key Concept

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

Topics

Linear Equations in One Variable

More questions from this topic