Questions: Solve the equation for (w) : the equation (-5(w-2)=-9 w+6)

Solve the equation for (w) : the equation (-5(w-2)=-9 w+6)
Transcript text: Solve the equation for $w$ : \[ \text { the equation }-5(w-2)=-9 w+6 \]
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Solution

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Solution Steps

Step 1: Expand the left side of the equation

\[ -5(w - 2) = -5w + 10 \]

Step 2: Rewrite the equation with the expanded form

\[ -5w + 10 = -9w + 6 \]

Step 3: Move all terms involving \( w \) to one side and constants to the other

Add \( 9w \) to both sides: \[ -5w + 9w + 10 = 6 \] Simplify: \[ 4w + 10 = 6 \]

Subtract \( 10 \) from both sides: \[ 4w = 6 - 10 \] Simplify: \[ 4w = -4 \]

Step 4: Solve for \( w \)

Divide both sides by \( 4 \): \[ w = \frac{-4}{4} \] Simplify: \[ w = -1 \]

Final Answer

\(\boxed{w = -1}\)

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