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Difficulty: MediumSolving One-Variable Linear Equations

Calculate the value of ww in the given linear equation:

Answer:3(2w+5)−4w=5(w−1)+2 3(2w + 5) - 4w = 5(w - 1) + 2

Value of ww: 【6】

Answer

The correct value for the variable is 6.
The correct answer is 6. Applying the distributive property to both sides simplifies the equation to 6w+15−4w=5w−5+26w + 15 - 4w = 5w - 5 + 2. Grouping like terms on each side yields 2w+15=5w−32w + 15 = 5w - 3. Subtracting 2w2w from both sides and adding 33 to both sides results in 18=3w18 = 3w. Dividing both sides by 3 isolates the variable, giving w=6w = 6.

Step-by-Step Solution

1
Distribute the constants across the terms inside the parentheses on both sides.
6w+15−4w=5w−5+26w + 15 - 4w = 5w - 5 + 2
To eliminate the parentheses and expose all terms for simplification.
2
Combine the like terms on each side of the equation independently.
2w+15=5w−32w + 15 = 5w - 3
To simplify both expressions before manipulating terms across the equals sign.
3
Move all variable terms to one side of the equation.
Subtract 2w2w from both sides to obtain 15=3w−315 = 3w - 3.
To group all the terms containing ww together and avoid negative coefficients.
4
Isolate the variable term and solve for ww.
Add 3 to both sides to get 18=3w18 = 3w, then divide by 3 to find w=6w = 6.
To determine the final numerical value of the variable.

Key Concept

Solving multi-step linear equations utilizing the distributive property and combining like terms.
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Topics

Solving One-Variable Linear Equations

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