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Math  /  Algebra

QuestionSolve for xx. 2(3x−6)=122(3 x-6)=12
Simplify your answer as much as possible. x=x=

Studdy Solution

STEP 1

1. The equation 2(3x−6)=12 2(3x - 6) = 12 is a linear equation in one variable.
2. The solution involves distributing, simplifying, and isolating the variable x x .

STEP 2

1. Distribute the constant outside the parentheses.
2. Simplify the equation.
3. Isolate the variable x x .
4. Check the solution by substituting it back into the original equation.

STEP 3

Distribute the 2 2 across the terms inside the parentheses:
2(3x−6)=2⋅3x−2⋅6 2(3x - 6) = 2 \cdot 3x - 2 \cdot 6
This simplifies to:
6x−12=12 6x - 12 = 12

STEP 4

Add 12 12 to both sides to start isolating the term with x x :
6x−12+12=12+12 6x - 12 + 12 = 12 + 12
This simplifies to:
6x=24 6x = 24

STEP 5

Divide both sides by 6 6 to solve for x x :
6x6=246 \frac{6x}{6} = \frac{24}{6}
This simplifies to:
x=4 x = 4

STEP 6

Check the solution by substituting x=4 x = 4 back into the original equation:
2(3(4)−6)=12 2(3(4) - 6) = 12
Simplify inside the parentheses:
2(12−6)=12 2(12 - 6) = 12
2⋅6=12 2 \cdot 6 = 12
12=12 12 = 12
Since both sides are equal, the solution is verified.
The solution is:
x=4 x = \boxed{4}

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