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Question

Difficulty: EasyLinear Equations in One Variable

If 12−2(w−1)=412 - 2(w - 1) = 4, what is the value of ww?

  1. A
    -3
  2. B
    3
  3. 5Answer
  4. D
    9

Answer

5
The correct answer is 5. We solve the equation by first distributing the coefficient −2-2 to (w−1)(w - 1), which yields 12−2w+2=412 - 2w + 2 = 4. Combining the constant terms gives 14−2w=414 - 2w = 4. Subtracting 14 from both sides results in −2w=−10-2w = -10. Finally, dividing by −2-2 isolates the variable, giving w=5w = 5.

Step-by-Step Solution

1
Distribute the negative coefficient −2-2 to the terms inside the parentheses.
12−2w+2=412 - 2w + 2 = 4
To eliminate the parentheses and simplify the expression.
2
Combine the constant terms on the left side of the equation.
14−2w=414 - 2w = 4
To group like terms together.
3
Subtract 14 from both sides of the equation.
−2w=−10-2w = -10
To isolate the variable term on one side of the equation.
4
Divide both sides of the equation by −2-2.
w=5w = 5
To find the value of ww.

Key Concept

Solving linear equations in one variable using distributive properties and basic operations.
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Topics

Linear Equations in One Variable

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