Question

which of the following represents the solution to (2x - 7 ge 9)?

a. a number line showing a closed circle at 8 with a shaded line extending to the left.
b. a number line showing a closed circle at 8 with a shaded line extending to the right.
c. a number line showing an open circle at 8 with a shaded line extending to the right.
d. a number line showing a closed circle at -8 with a shaded line extending to the left.

Explanation:

⚡ Using what you learned: solving two-step and multi-step inequalities

Step 1: Solve the inequality

Solve the given inequality:

$$ 2x - 7 \ge 9 $$

Add \( 7 \) to both sides:

$$ 2x \ge 16 $$

Divide by \( 2 \):

$$ x \ge 8 $$

Step 2: Match with the correct graph

The inequality \( x \ge 8 \) is represented on a number line by:

• A solid circle at \( 8 \) (since the inequality includes "or equal to", \(\ge\)).
• An arrow pointing to the right (representing all values greater than or equal to \( 8 \)).

Looking at the options:

• A shows a segment between two points.
• B shows a solid circle at \( 8 \) with an arrow pointing to the right.
• C shows a solid circle at a different value pointing to the right.
• D shows an arrow pointing to the left.

Therefore, option B is the correct representation.

Answer:

B