Questions: Linear Equations Introduction to solving an equation with parenti Solve for (w). [3(3w-5)=12] Simplify your answer as much as possible. [w=]

Linear Equations Introduction to solving an equation with parenti Solve for (w). [3(3w-5)=12] Simplify your answer as much as possible. [w=]
Transcript text: Linear Equations Introduction to solving an equation with parenti Solve for $w$. \[ 3(3 w-5)=12 \] Simplify your answer as much as possible. \[ w= \] $\square$ Explanation Check
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Solution

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Solution Steps

To solve the equation \(3(3w - 5) = 12\), we first need to distribute the 3 across the terms inside the parentheses. This will give us a linear equation in terms of \(w\). Next, we will isolate \(w\) by performing algebraic operations such as addition, subtraction, multiplication, or division as needed.

Step 1: Distribute the Terms

We start with the equation: \[ 3(3w - 5) = 12 \] Distributing the 3 gives: \[ 9w - 15 = 12 \]

Step 2: Isolate the Variable

Next, we add 15 to both sides to isolate the term with \(w\): \[ 9w - 15 + 15 = 12 + 15 \] This simplifies to: \[ 9w = 27 \]

Step 3: Solve for \(w\)

Now, we divide both sides by 9 to solve for \(w\): \[ w = \frac{27}{9} \] This simplifies to: \[ w = 3 \]

Final Answer

\(\boxed{w = 3}\)

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