Solve Two-Step Inequalities Quick Check

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

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.

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.

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.

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.
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Answer 1

To solve the inequality \(9.5x - 1.25 < 32\), 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: \[ x < \frac{33.25}{9.5} \] \[ x < 3.5 \]

Now, let's interpret the result. The solution means \(x\) can take any value less than \(3.5\).

On a number line:

• There should be an open point (to indicate that \(3.5\) is not included).
• The arrow should point to the left, showing all values less than \(3.5\).

From the options provided, the correct graph will have an open point between \(3\) and \(4\) (specifically near \(3.5\)), with a leftward arrow extending indefinitely towards negative infinity.

If you describe the relevant options, you should select the one that fits this description. The correct answer is the one that has an open point around \(3.5\) and an arrow pointing left.