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 $\square$

Solution

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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