Question

solve the inequality and graph the solution.
q - 2 ≤ 2
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.
(number line with ticks at 0,1,2,3,4,5,6,7)

Explanation:

Step1: Add 2 to both sides

To solve the inequality \( q - 2 \leq 2 \), we add 2 to both sides of the inequality. This is based on the addition property of inequalities, which states that if we add the same number to both sides of an inequality, the inequality sign remains the same.

$$ q - 2 + 2 \leq 2 + 2 $$

Step2: Simplify both sides

Simplifying the left - hand side \( q-2 + 2\) gives \( q \), and simplifying the right - hand side \( 2 + 2\) gives 4. So we have:

$$ q\leq4 $$

For graphing the solution:

• The endpoint of the ray is at \( q = 4 \). Since the inequality is \( q\leq4 \) (the "less than or equal to" sign), the endpoint at 4 is a closed circle (to indicate that 4 is included in the solution set).
• The arrow of the ray points to the left (towards negative infinity) because we are looking for all values of \( q \) that are less than or equal to 4.

Answer:

The solution to the inequality \( q - 2\leq2 \) is \( q\leq4 \). To graph it, plot a closed circle at 4 on the number line and draw an arrow pointing to the left.