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Difficulty: MediumSolving One-Variable Linear Equations

What is the value of kk that makes the following equation true?

4(k−2)−3k=5k−2(k+10) 4(k - 2) - 3k = 5k - 2(k + 10)
  1. 6Answer
  2. B
    4
  3. C
    3
  4. D
    -14

Answer

The correct value for the variable is 6.
By following the correct order of operations, distributing carefully, and balancing the equation, we find that k = 6 makes both sides of the equation equal.

Step-by-Step Solution

1
Distribute the values outside the parentheses on both sides of the equation.
4k−8−3k=5k−2k−20 4k - 8 - 3k = 5k - 2k - 20
Applying the distributive property removes the parentheses and allows for combining like terms.
2
Combine like terms on each side of the equation.
k−8=3k−20 k - 8 = 3k - 20
Simplifying each side individually makes it easier to isolate the variable.
3
Subtract kk from both sides to collect the variables on the right side.
−8=2k−20 -8 = 2k - 20
Balancing the equation by performing the inverse operation isolates the variable terms on one side.
4
Add 20 to both sides to isolate the variable term.
12=2k 12 = 2k
Moving the constants to the opposite side of the variable completes the isolation process.
5
Divide both sides by 2.
k=6 k = 6
Dividing by the coefficient gives the final value of the variable.

Key Concept

Solving multi-step linear equations involves distributing, combining like terms, and balancing the equation using inverse operations.
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Topics

Solving One-Variable Linear Equations

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