Question

solve the inequality and graph the solution on the line provided.

\\5x + 17 \ge 52\\

answer attempt 2 out of 2

inequality notation:

number line:

Explanation:

Subtract 17 from both sides

To isolate the variable term, subtract 17 from both sides of the inequality.

$$ 5x + 17 - 17 \ge 52 - 17 $$

$$ 5x \ge 35 $$

Divide both sides by 5

To solve for \(x\), divide both sides by 5. Since 5 is positive, the inequality sign remains the same.

$$ \frac{5x}{5} \ge \frac{35}{5} $$

$$ x \ge 7 $$

Determine the number line representation

The inequality \(x \ge 7\) includes all numbers greater than or equal to 7.

• A solid circle is placed at 7 because the inequality is non-strict (\(\ge\)).
• An arrow is drawn pointing to the right to represent all values greater than 7.

Answer:

Solve the inequality and graph the solution on the line provided.

\(5x + 17 \ge 52\)

Inequality Notation: <blank>\(x \ge 7\)</blank>