Question

1. write an inequality for the graph.

1. circle all of the values that are included in the solution set of the inequality ( x - 3 > -2.5 ).

( -2 ) ( -0.5 ) ( 0 ) ( 0.5 ) ( 1 ) ( 3 )

1. solve the inequality and graph the solution: ( 2x + 7 < 3 ).

Explanation:

Question 1

Step1: Analyze the graph

The graph has a closed dot at -3 and an arrow pointing to the right, which means the solution includes -3 and all numbers greater than -3.

Step2: Write the inequality

For a closed dot, we use $\geq$ (or $\leq$ depending on direction). Since the arrow is to the right (increasing values), the inequality is $x \geq -3$.

Step1: Solve the inequality

Start with $x - 3 > -2.5$. Add 3 to both sides: $x - 3 + 3 > -2.5 + 3$.

Step2: Simplify

Simplifying gives $x > 0.5$. Now check which values are greater than 0.5: -2 (no), -0.5 (no), 0 (no), 0.5 (no, since it's > not ≥), 1 (yes), 3 (yes).

Step1: Solve the inequality

Start with $2x + 7 < 3$. Subtract 7 from both sides: $2x + 7 - 7 < 3 - 7$.

Step2: Simplify

Simplifying gives $2x < -4$. Divide both sides by 2: $\frac{2x}{2} < \frac{-4}{2}$.

Step3: Final solution

Simplifying gives $x < -2$. For the graph, draw an open dot at -2 (since the inequality is <, not ≤) and an arrow pointing to the left (towards smaller numbers).

Answer:

$x \geq -3$

Question 2