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Question

Difficulty: EasyLinear Equations in One Variable

If 20−2(x+3)=820 - 2(x + 3) = 8, what is the value of xx?

  1. A
    -11
  2. B
    -3
  3. 3Answer
  4. D
    9

Answer

3
The correct answer is 3. Distributing −2-2 to the terms inside the parentheses gives 20−2x−6=820 - 2x - 6 = 8. Simplifying the left side yields 14−2x=814 - 2x = 8. Subtracting 14 from both sides results in −2x=−6-2x = -6. Dividing both sides by −2-2 gives x=3x = 3.

Step-by-Step Solution

1
Distribute the coefficient −2-2 to all terms inside the parentheses (x+3)(x + 3).
20−2x−6=820 - 2x - 6 = 8
Applying the distributive property requires multiplying both xx and 33 by −2-2.
2
Combine the constant terms 2020 and −6-6 on the left side of the equation.
14−2x=814 - 2x = 8
Simplifying the expression makes it easier to isolate the variable term.
3
Subtract 1414 from both sides of the equation to isolate the variable term −2x-2x.
−2x=−6-2x = -6
This moves the constant term to the opposite side of the equation.
4
Divide both sides of the equation by −2-2 to solve for xx.
x=3x = 3
Dividing by the coefficient of the variable isolates the variable completely.

Key Concept

Solving linear equations in one variable with parentheses by distributing coefficients, combining like terms, and isolating the variable.
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Topics

Linear Equations in One Variable

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