Question

solve the inequality and graph the solution.
q - 3 ≥ 4
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.
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Explanation:

Step1: Isolate the variable \( q \)

To solve the inequality \( q - 3 \geq 4 \), we add 3 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 direction of the inequality remains the same.

$$ q - 3 + 3 \geq 4 + 3 $$

Step2: Simplify both sides

Simplifying the left - hand side, \( q-3 + 3=q \). Simplifying the right - hand side, \( 4 + 3 = 7 \). So we get \( q\geq7 \).

For graphing the solution:

• The endpoint of the ray is at 7. Since the inequality is \( \geq \), the endpoint is a closed circle (because 7 is included in the solution set).
• The arrow of the ray points to the right (towards positive infinity) because we are looking for all values of \( q \) that are greater than or equal to 7.

Answer:

The solution to the inequality \( q - 3\geq4 \) is \( q\geq7 \). To graph the solution, plot a closed circle at 7 on the number line and draw an arrow pointing to the right.