To solve the inequality and identify the correct graph, let's analyze the inequality step-by-step:

Given Inequality:

$-2x + 7 < 23$

Step 1: Isolate $x$

1. Subtract 7 from both sides: $-2x < 16$
2. Divide by -2 (and remember to reverse the inequality since we are dividing by a negative number): $x > -8$

Solution Set

The solution to the inequality is: $x > -8$

Interpreting the Graph

• We are looking for a graph that represents $x > -8$, which should be an open circle at -8 (indicating that -8 is not included) and a line extending to the right (since $x$ is greater than -8).

Choosing the Correct Option

• Option B represents the correct solution. It shows an open circle at -8 and an arrow extending to the right.

Answer:

The correct answer is B.

Would you like further details or have any questions?

Here are five related questions to deepen understanding:

1. How do you handle inequalities when multiplying or dividing by a negative number?
2. What would the graph look like if the inequality was $x \geq -8$?
3. How would the solution change if the inequality was $-2x + 7 \leq 23$?
4. What if the inequality was $2x + 7 < 23$ instead?
5. How can inequalities be represented on a number line when using intervals?

Tip: Remember, whenever dividing or multiplying by a negative in inequalities, flip the inequality sign!