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

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

Solution

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: $w = -1$

$\boxed{w = -1}$

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