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Difficulty: MediumSolving One-Variable Linear Equations

An algebraic equation is shown below.

4(x−3)−2x=5x−27 4(x - 3) - 2x = 5x - 27

Which of the following represents the correct value of xx?

  1. 5Answer
  2. B
    13
  3. C
    8
  4. D
    -15

Answer

5
The correct answer is derived by first distributing the 4 to get 4x−124x - 12. Combining 4x4x and −2x-2x yields 2x−122x - 12. Moving the variables to one side (5x−2x=3x5x - 2x = 3x) and the constants to the other (−12+27=15-12 + 27 = 15) results in 15=3x15 = 3x. Dividing by 3 gives the final result of x=5x = 5.

Step-by-Step Solution

1
Distribute the coefficient 4 into the parentheses.
4x−12−2x=5x−27 4x - 12 - 2x = 5x - 27
According to the distributive property, the number outside the parentheses must multiply each term inside.
2
Combine the like terms on the left side of the equation.
2x−12=5x−27 2x - 12 = 5x - 27
The terms 4x4x and −2x-2x are like terms and subtract to form 2x2x.
3
Isolate the variable terms on one side by subtracting 2x2x from both sides.
−12=3x−27 -12 = 3x - 27
Subtracting 2x2x from both sides keeps the equation balanced and groups all terms containing xx on the right side.
4
Isolate the variable xx by adding 27 to both sides.
15=3x 15 = 3x
Adding 27 cancels out the −27-27 on the right, leaving the variable term by itself.
5
Solve for xx by dividing both sides by 3.
x=5 x = 5
Dividing by the coefficient of xx provides the final value of the unknown variable.

Key Concept

Solving linear equations requires correctly applying the distributive property, combining like terms accurately, and using inverse operations equally on both sides to isolate the variable.
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Topics

Solving One-Variable Linear Equations

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