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Difficulty: MediumSolving One-Variable Linear Equations

Solve the following linear equation for ww:

13(12w−9)+5=2(w−1)+8 \frac{1}{3}(12w - 9) + 5 = 2(w - 1) + 8

Enter the exact integer value that satisfies the equation.

Answer:The value of ww is 【2】.

Answer

2
By successfully distributing the factors, combining like terms on each side, and balancing the equation by moving variables and constants to opposite sides, the isolated variable equates to exactly 2.

Step-by-Step Solution

1
Distribute the coefficients to remove parentheses on both sides of the equation.
4w−3+5=2w−2+84w - 3 + 5 = 2w - 2 + 8
Applying the distributive property simplifies the expression and exposes the variable terms.
2
Combine the constant terms on each side.
4w+2=2w+64w + 2 = 2w + 6
Simplifying each side makes it easier to balance the equation in the next steps.
3
Subtract 2w2w from both sides of the equation.
2w+2=62w + 2 = 6
This groups all the variable terms onto the left side.
4
Subtract 22 from both sides, then divide the result by 22.
2w=4⇒w=22w = 4 \Rightarrow w = 2
This completely isolates the variable ww to reveal its final value.

Key Concept

Solving One-Variable Linear Equations
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Topics

Solving One-Variable Linear Equations

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