Question

which graph represents the solution set of this inequality?
-2x + 7 < 23
choose 1 answer:
a
<---(-10)-(-9)-(-8)(open circle)-(-7)-(-6)-(-5)-(-4)-(-3)-(-2)-(-1)-0-1-2-3-4-5--->
b
<---(-5)-(-4)-(-3)-(-2)-(-1)-0-1-2-3-4-5-6-7-(open circle)-...--->
show solution and move

Explanation:

Step1: Solve the inequality

Subtract 7 from both sides: $-2x + 7 - 7 < 23 - 7$ → $-2x < 16$.
Divide both sides by -2 (reverse inequality sign): $\frac{-2x}{-2} > \frac{16}{-2}$ → $x > -8$.

Step2: Analyze the graphs

The solution $x > -8$ means an open circle at -8 (since it's not "≤" or "≥") and a line to the right of -8.
Graph A has a line to the left of -8 (incorrect). Graph B (assuming the open circle is at -8? Wait, no—wait, the first graph (A) has open circle at -8, line left? No, wait, the first graph's arrow is left, but our solution is $x > -8$ (arrow right). Wait, maybe the user's graph B has open circle at -8 with arrow right? Wait, no, the first graph (A) shows open circle at -8, line to the left (x < -8), which is wrong. Wait, let's recheck:

Wait, solving $-2x +7 <23$:
-2x < 16 → x > -8 (because dividing by negative flips inequality). So the graph should have open circle at -8, and line to the right (towards positive numbers). Wait, but the first graph (A) has arrow left (x < -8), which is wrong. Wait, maybe the second graph (B) has open circle at -8? Wait, the user's B graph: the numbers are -5, -4,... up to 8? Wait, maybe a typo. Wait, the correct solution is $x > -8$, so the graph with open circle at -8 and arrow to the right. But in the given options, if A is open circle at -8, arrow left (x < -8) and B is open circle at -8, arrow right (x > -8), then B is correct. But wait, the user's A graph: numbers -10, -9, -8 (open circle), arrow left. B graph: numbers -5, -4,... 8 (open circle), arrow right? Wait, maybe the B graph's open circle is at -8? Wait, maybe the user's B graph has the open circle at -8 (but labeled as 8? No, maybe a typo). Wait, regardless, the solution is $x > -8$, so the graph with open circle at -8 and arrow to the right. So if B is that, then B. But wait, the first graph (A) is arrow left (x < -8), which is wrong. So the correct graph is the one with open circle at -8 and arrow right, which should be option A? No, wait, no: when we solve $-2x +7 <23$, we get $x > -8$. So the graph should have an open circle at -8 (since it's a strict inequality) and the line should go to the right (towards positive numbers). So if A is arrow left (x < -8) and B is arrow right (x > -8), then B is correct. But in the user's A graph, the open circle is at -8, arrow left (x < -8) – that's incorrect. So the correct answer is the graph with open circle at -8 and arrow right, which is option B (assuming B has that). Wait, maybe the user's B graph has the open circle at -8 (but the numbers are mislabeled). Anyway, the solution is $x > -8$, so the graph with open circle at -8 and arrow to the right. So the correct answer is the graph that represents $x > -8$, which is the one with open circle at -8 and arrow right (likely option B, but need to check the graphs again). Wait, maybe the user's A is x < -8 (wrong) and B is x > -8 (correct). So the answer is B. But wait, let's confirm:

Solving the inequality:

1. Subtract 7: $-2x < 16$
2. Divide by -2 (flip inequality): $x > -8$

So the solution set is all real numbers greater than -8. The graph should have an open circle at -8 (since -8 is not included) and a line extending to the right (towards positive infinity). So the correct graph is the one with open circle at -8 and arrow to the right, which is option B (assuming B is that).

Answer:

B. (The graph with open circle at -8 and arrow to the right)