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Difficulty: MediumSolving One-Variable Linear Equations

Consider the following equation:

4(v−2)+6=7v−2(v+5) 4(v - 2) + 6 = 7v - 2(v + 5)

What is the value of vv that satisfies this equation?

  1. A
    12
  2. B
    -12
  3. 8Answer
  4. D
    -4

Answer

8
Expanding the terms by distributing gives 4v - 8 + 6 = 7v - 2v - 10. Simplifying both sides yields 4v - 2 = 5v - 10. By subtracting 4v from both sides and adding 10 to both sides, the variable v is isolated to yield 8.

Step-by-Step Solution

1
Distribute the constants into the parentheses on both sides of the equation.
4v - 8 + 6 = 7v - 2v - 10
This removes the parentheses and expands the expressions so like terms can be combined.
2
Combine the constant terms on the left side and the variable terms on the right side.
4v - 2 = 5v - 10
Simplifying both sides makes it easier to isolate the variable.
3
Subtract 4v from both sides to group the variable terms on the right side.
-2 = v - 10
This step groups the variables together while keeping the coefficient of v positive.
4
Add 10 to both sides to solve for v.
8 = v
This step fully isolates v, giving the final solution.

Key Concept

Solving linear equations involves distributing constants to expand expressions, combining like terms, and performing identical operations on both sides to isolate the unknown variable.
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Topics

Solving One-Variable Linear Equations

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