Solve the inequality 9.5x−1.25

Question

Solve the inequality 9.5x−1.25<32
. Which of the following graphs shows the solution?(1 point)
Responses

1.A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line between 3 and 4. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10.
Image with alt text: A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line between 3 and 4. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10.

2.A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 4 and 5, just before 5. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10.
Image with alt text: A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 4 and 5, just before 5. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10.

3.A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line between 3 and 4, just after the 3. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10.
Image with alt text: A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line between 3 and 4, just after the 3. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10.

4.A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 3 and 4. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10.
Image with alt text: A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 3 and 4. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10.

GPT-4o mini · Answer

To solve the inequality $ 9.5x - 1.25 < 32 $, we can follow these steps: 1. **Add 1.25 to both sides:** $$ 9.5x < 32 + 1.25 $$ $$ 9.5x < 33.25 $$ 2. **Divide both sides by 9.5:** $$ x < \frac{33.25}{9.5} $$ $$ x < 3.5 $$ So the solution to the inequality is $ x < 3.5 $. Next, we need to represent this solution on a number line. - Since the solution is $ x < 3.5 $, it will be represented with an **open point** at 3.5 (indicating that 3.5 is not included in the solution) and an arrow extending left to indicate all values less than 3.5. Looking at the options you provided: 1. The first option has an open point plotted between 3 and 4, which is correct for $ x < 3.5 $. 2. The second option has a closed point, which is incorrect because we have an open interval. 3. The third option has an open point just after 3, which also indicates $ x < 3.5 $ but may be slightly misleading. 4. The fourth option has a closed point, which is incorrect. The best representation of the solution $ x < 3.5 $ is: **Option 1**: A number line with an open point between 3 and 4 and a leftward arrow beyond negative 10.