Questions: Solve the following linear equation. Express your answer as an integer or a simplified fraction. 2w + 20 = 8w + 20

Solve the following linear equation. Express your answer as an integer or a simplified fraction. 2w + 20 = 8w + 20
Transcript text: Solve the following linear equation. Express your answer as an integer or a simplified fraction. \[ 2 w+20=8 w+20 \]
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Solution

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Solution Steps

To solve the linear equation \(2w + 20 = 8w + 20\), we need to isolate the variable \(w\). This involves moving all terms involving \(w\) to one side of the equation and constant terms to the other side. Then, we simplify to find the value of \(w\).

Step 1: Set Up the Equation

We start with the given linear equation: \[ 2w + 20 = 8w + 20 \]

Step 2: Move All Terms Involving \( w \) to One Side

Subtract \( 2w \) from both sides: \[ 20 = 6w + 20 \]

Step 3: Isolate the Variable \( w \)

Subtract 20 from both sides: \[ 0 = 6w \]

Step 4: Solve for \( w \)

Divide both sides by 6: \[ w = 0 \]

Final Answer

\[ \boxed{w = 0} \]

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