Questions: Solving Equations Algebraic Expressions Solve the equation and simplify your answer. 3(x-1)=2(3-x) x=[?]/square

Solving Equations Algebraic Expressions Solve the equation and simplify your answer. 3(x-1)=2(3-x) x=[?]/square
Transcript text: Solving Equations Algebraic Expressions Solve the equation and simplify your answer. \[ \begin{array}{c} 3(x-1)=2(3-x) \\ x=\frac{[?]}{\square} \end{array} \]
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Solution

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Solution Steps

To solve the equation \(3(x-1) = 2(3-x)\), we will first expand both sides of the equation. Then, we will collect all terms involving \(x\) on one side and constant terms on the other side. Finally, we will solve for \(x\) by isolating it.

Step 1: Expand Both Sides

We start with the equation: \[ 3(x - 1) = 2(3 - x) \] Expanding both sides gives: \[ 3x - 3 = 6 - 2x \]

Step 2: Collect Like Terms

Next, we will collect all terms involving \(x\) on one side and constant terms on the other side. Adding \(2x\) to both sides and adding \(3\) to both sides results in: \[ 3x + 2x = 6 + 3 \] This simplifies to: \[ 5x = 9 \]

Step 3: Solve for \(x\)

Now, we isolate \(x\) by dividing both sides by \(5\): \[ x = \frac{9}{5} \]

Final Answer

\(\boxed{x = \frac{9}{5}}\)

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