Questions: Solve for (x). Enter the solutions from least to greatest. ((3 x-6)(-x+3)=0) lesser (x=) greater (x=)

Solve for (x). Enter the solutions from least to greatest. ((3 x-6)(-x+3)=0) lesser (x=) greater (x=)
Transcript text: Solve for $x$. Enter the solutions from least to greatest. \[ \begin{array}{l} (3 x-6)(-x+3)=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array} \]
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Solution

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Solution Steps

To solve the equation \((3x-6)(-x+3)=0\), we need to find the values of \(x\) that make each factor equal to zero. This involves setting each factor equal to zero and solving for \(x\). Once we have the solutions, we will order them from least to greatest.

Step 1: Set Each Factor to Zero

We start with the equation \((3x-6)(-x+3)=0\). To find the values of \(x\), we set each factor equal to zero:

  1. \(3x - 6 = 0\)
  2. \(-x + 3 = 0\)
Step 2: Solve Each Equation

For the first equation \(3x - 6 = 0\): \[ 3x = 6 \implies x = \frac{6}{3} = 2 \]

For the second equation \(-x + 3 = 0\): \[ -x = -3 \implies x = 3 \]

Step 3: Order the Solutions

The solutions we found are \(x = 2\) and \(x = 3\). We order them from least to greatest: \[ 2 < 3 \]

Final Answer

The lesser solution is \(x = 2\) and the greater solution is \(x = 3\). Thus, we can express the final answer as: \[ \boxed{x = 2 \text{ and } x = 3} \]

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