Solve 8x>24

Question

.(1 point)
Responses

x>16
x greater than 16

x<16
x less than 16

x<3
x less than 3

x>3

Solve x13<45
.(1 point)
Responses

x>525
x greater than Start Fraction 52 over 5 End Fraction

x<1025
x less than 10 Start Fraction 2 over 5 End Fraction

x<1345
x less than 13 Start Fraction 4 over 5 End Fraction

x<465

Question
Solve the inequality 4x>10
. Which of the following graphs shows the solution? (1 point)
Responses

A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 2.5. A rightward arrow is marked on the number line that originates at the open circle and goes beyond 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 2.5. A rightward arrow is marked on the number line that originates at the open circle and goes beyond 10.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 6. A leftward arrow is marked on the number line that originates at the open circle and goes beyond negative 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 6. A leftward arrow is marked on the number line that originates at the open circle and goes beyond negative 10.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 2.5. A leftward arrow is marked on the number line that originates at the open circle and goes beyond negative 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 2.5. A leftward arrow is marked on the number line that originates at the open circle and goes beyond negative 10.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 6. A rightward arrow is marked on the number line that originates at the open circle and goes beyond 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 6. A rightward arrow is marked on the number line that originates at the open circle and goes beyond 10.

Use the image to answer the question.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 1.75. A leftward arrow is marked on the number line that originates at the open circle and goes beyond negative 10.

Nora solved an inequality and graphed the solution on the number line. Which of the following inequalities did she solve?

(1 point)
Responses

4x>7
4 x greater than 7

1.75x<3.5
1.75 x less than 3.5

8x>14
8 x greater than 14

6x<10.5
6 x less than 10.5
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Question
Solve the inequality 23x≤5
. Which of the following graphs shows the solution? (1 point)
Responses

A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 5 start fraction 2 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 5 start fraction 2 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 4 start fraction 1 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 4 start fraction 1 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 3 start fraction 1 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 3 start fraction 1 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 7.5. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 7.5. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
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Answer 1

Let's solve each of the inequalities you provided step by step.

1. For the inequality 8x > 24:

   To isolate x, divide both sides by 8: \[ x > 3 \]

   The correct response is:

   • x > 3

2. For the inequality x/13 < 45:

   To isolate x, multiply both sides by 13: \[ x < 45 \times 13 \] \[ x < 585 \] So, the response is:

   • x < 585 (which can be related back to the options given, but since they seem to be incomplete, the final answer is valid as 585)

3. For the inequality 4x > 10:

   To isolate x, divide both sides by 4: \[ x > \frac{10}{4} \] \[ x > 2.5 \]

   The corresponding graph would show an open circle at 2.5 with an arrow extending to the right. The correct graph would be:

   • A number line ranges from negative 10 to 10 with an open point at 2.5 with a rightward arrow.

4. For the graph question regarding Nora, we note that the open circle and leftward arrow indicate a value that is less than a certain number. Since the closed point at 1.75 suggests x is less than or equal to 1.75, this confirms:

   The inequality is:

   • 4x > 7

5. For the inequality (23/3)x ≤ 5:

   To isolate x, multiply both sides by 3/23: \[ x \leq \frac{5 \cdot 3}{23} = \frac{15}{23} \]

   Thus, the leftmost point on the graph (closed circle) would be at approximately 0.652 (which should be given in the fraction format). Therefore, we consider a closed point at \(5 \frac{2}{3}\).

   The correct response is:

   • A closed point is plotted on the number line at \(5 \frac{2}{3}\) with a leftward arrow.

Please confirm the ranges and specific values with the answered graphs to ensure they align with the right choices as indicated by the solutions presented.