Questions: Solve the inequality. Express your answer using set notation and interval notation. Graph the solution set. 3 x-3 ≥ 7+x The solution is expressed in set notation as x . The solution is expressed in interval notation as

Solve the inequality. Express your answer using set notation and interval notation. Graph the solution set. 3 x-3 ≥ 7+x The solution is expressed in set notation as x . The solution is expressed in interval notation as
Transcript text: Solve the inequality. Express your answer using set notation and interval notation. Graph the solution set. \[ 3 x-3 \geq 7+x \] The solution is expressed in set notation as $\{x \mid$ $\square$ \}. The solution is expressed in interval notation as $\square$
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Solution

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Solution Steps

Step 1: Solve the inequality

First, we solve the inequality \(3x - 3 \geq 7 + x\).

\[ 3x - 3 \geq 7 + x \]

Subtract \(x\) from both sides:

\[ 2x - 3 \geq 7 \]

Add 3 to both sides:

\[ 2x \geq 10 \]

Divide both sides by 2:

\[ x \geq 5 \]

Step 2: Express the solution in set notation

The solution in set notation is:

\[ \{x \mid x \geq 5\} \]

Step 3: Express the solution in interval notation

The solution in interval notation is:

\[ [5, \infty) \]

Final Answer

The solution is expressed in set notation as \(\{x \mid x \geq 5\}\).

The solution is expressed in interval notation as \([5, \infty)\).

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