Solve Multiplication Inequalities Quick Check
1 of 51 of 5 Items
Question
Solve 8x>24 .(1 point)
Responses
x<3
x less than 3
x>3
x greater than 3
x<16
x less than 16
x>16
Solve x/13<4/5.(1 point)
Responses
x<4/65
x less than Start Fraction 4 over 65 End Fraction
x<10 2/5
x less than 10 Start Fraction 2 over 5 End Fraction
x>52/5
x greater than Start Fraction 52 over 5 End Fraction
x<13 4/5
x less than 13 Start Fraction 4 over 5 End Fraction
do both
Sure!
For the first inequality, 8x > 24, divide both sides by 8 to isolate x:
8x / 8 > 24 / 8
x > 3
So the solution is x > 3.
For the second inequality, x/13 < 4/5, multiply both sides by 13 to get rid of the fraction:
(x/13) * 13 < (4/5) * 13
x < (4/5) * 13
Simplifying the right side:
x < (52/5)
So the solution is x < 52/5.
Therefore, the correct answer choices are:
- x greater than 3 for the first inequality
- x less than 52/5 for the second inequality.
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 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.
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.
To solve the inequality 4x > 10, we need to divide both sides by 4:
4x / 4 > 10 / 4
x > 2.5
So the solution to the inequality is x > 2.5.
Therefore, the correct answer is the graph that shows a number line ranging from -10 to 10 with numbers listed in unit increments, and an open point plotted at 2.5. 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
8x>14
8 x greater than 14
6x<10.5
6 x less than 10.5
4x>7
4 x greater than 7
1.75x<3.5
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 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.
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.
Based on the given image, the correct answers are as follows:
For the first question, Nora solved the inequality 6x < 10.5. This is because the open point is plotted on the number line at 1.75 and there is a leftward arrow marked on the number line that originates at the open circle and goes beyond negative 10. Therefore, the correct answer is 6x < 10.5.
For the second question, the correct graph showing the solution to the inequality 23x ≤ 5 is the one where a closed point is plotted on the number line at 4 1/3. There is a leftward arrow marked on the number line that originates at the closed circle and goes beyond negative 10. Therefore, the correct answer is the graph with the closed point at 4 1/3.