Question

solve the inequality and graph the solution set on a number line.
3x - 3 > -x + 17

Explanation:

Step1: Add \(x\) to both sides

To isolate the variable terms, we add \(x\) to each side of the inequality \(3x - 3 > -x + 17\). This gives us \(3x + x - 3 > -x + x + 17\), which simplifies to \(4x - 3 > 17\).

Step2: Add 3 to both sides

Next, we add 3 to both sides to isolate the term with \(x\). So, \(4x - 3 + 3 > 17 + 3\), which simplifies to \(4x > 20\).

Step3: Divide by 4

Now, we divide both sides by 4 to solve for \(x\). \(\frac{4x}{4} > \frac{20}{4}\), which simplifies to \(x > 5\).

To graph the solution set on a number line:

• Draw a number line.
• Place an open circle at 5 (since \(x\) is not equal to 5, only greater than).
• Draw an arrow to the right of 5 to represent all numbers greater than 5.

Answer:

The solution to the inequality \(3x - 3 > -x + 17\) is \(x > 5\). The graph has an open circle at 5 and an arrow pointing to the right.