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Solve for \( w \). \[ 15=3 w+6(w-8) \] Simplify your answer as much as possible. \( w=\prod \)

Ask by Pope Riley. in the United States
Feb 20,2025

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Answer

\( w=7 \)

Solution

Solve the equation \( 15=3w+6(w-8) \). Solve the equation by following steps: - step0: Solve for \(w\): \(15=3w+6\left(w-8\right)\) - step1: Swap the sides: \(3w+6\left(w-8\right)=15\) - step2: Move the expression to the left side: \(3w+6\left(w-8\right)-15=0\) - step3: Calculate: \(9w-63=0\) - step4: Move the constant to the right side: \(9w=0+63\) - step5: Remove 0: \(9w=63\) - step6: Divide both sides: \(\frac{9w}{9}=\frac{63}{9}\) - step7: Divide the numbers: \(w=7\) The solution to the equation \(15=3w+6(w-8)\) is \(w=7\).

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The Deep Dive

To solve for \( w \) in the equation \( 15 = 3w + 6(w - 8) \), we first distribute the 6 in the second term: \[ 15 = 3w + 6w - 48 \] Now, combine like terms: \[ 15 = 9w - 48 \] Next, add 48 to both sides: \[ 15 + 48 = 9w \] This simplifies to: \[ 63 = 9w \] Now, divide both sides by 9 to isolate \( w \): \[ w = \frac{63}{9} \] Simplifying this fraction gives: \[ w = 7 \] Thus, the solution is: \[ w = 7 \]

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