To solve the inequality 4/7x - 2/7 > 5/7, we need to isolate the variable x.
Adding 2/7 to both sides of the inequality, we have:
4/7x - 2/7 + 2/7 > 5/7 + 2/7
This simplifies to:
4/7x > 7/7
Now, we can divide both sides of the inequality by 4/7:
(4/7x)/(4/7) > (7/7)/(4/7)
This simplifies to:
x > 7/4
Since the inequality is x > 7/4, we can write the rational number as a mixed number by dividing the numerator (7) by the denominator (4):
7 ÷ 4 = 1 remainder 3
So, x > 1 3/4.
Solve 4/7x−2/7>5/7 . Write the rational number in your answer as a mixed number. Make sure to write your inequality so that x comes first.
11 answers
Solve 5x+12.5<23.1 . Write the rational number in your answer in decimal form to the hundredths place. Make sure to write your inequality so that x comes first.
To solve the inequality 5x + 12.5 < 23.1, we need to isolate the variable x.
First, subtract 12.5 from both sides of the inequality:
5x + 12.5 - 12.5 < 23.1 - 12.5
This simplifies to:
5x < 10.6
Now, we can divide both sides of the inequality by 5:
(5x)/5 < (10.6)/5
This simplifies to:
x < 2.12
So, the rational number in decimal form to the hundredths place is x < 2.12.
First, subtract 12.5 from both sides of the inequality:
5x + 12.5 - 12.5 < 23.1 - 12.5
This simplifies to:
5x < 10.6
Now, we can divide both sides of the inequality by 5:
(5x)/5 < (10.6)/5
This simplifies to:
x < 2.12
So, the rational number in decimal form to the hundredths place is x < 2.12.
Use the image to answer the question.
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 after 4. A rightward arrow is marked on the number line that originates at the closed point and goes beyond 10.
What linear inequality is shown graphed on the number line? Make sure to write your inequality so that x comes first.
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 after 4. A rightward arrow is marked on the number line that originates at the closed point and goes beyond 10.
What linear inequality is shown graphed on the number line? Make sure to write your inequality so that x comes first.
Based on the description of the image, the closed point between 4 and 5 represents a number greater than or equal to 4. The rightward arrow extending beyond 10 indicates that the numbers satisfying the inequality continue beyond 10.
Therefore, the linear inequality shown graphed on the number line is:
x ≥ 4
Therefore, the linear inequality shown graphed on the number line is:
x ≥ 4
Use the image to answer the question.
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 4.25, just after 4. A rightward arrow is marked on the number line that originates at the closed point and goes beyond 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 4.25, just after 4. A rightward arrow is marked on the number line that originates at the closed point and goes beyond 10.
Based on the image, the closed point at 4.25 represents a number greater than 4 but less than 4.5. The rightward arrow extending beyond 10 indicates that the numbers satisfying the inequality continue beyond 10.
Therefore, the linear inequality shown graphed on the number line is:
4 < x < 4.5
Therefore, the linear inequality shown graphed on the number line is:
4 < x < 4.5
Solve Two-Step Inequalities Practice
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5 of 55 of 5 Items
Question
Use the image to answer the question.
Four number lines are shown labeled from 1 to 4 vertically one below the other. The number lines range from negative 10 to 10 with numbers listed in unit increments. The first number line has a closed point marked on 5. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10. The second number line has an open point marked on 5. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10. The third number line has a closed point plotted on the number line between 4 and 5, just after the 4. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10. The fourth number line has an open point plotted on the number line between 4 and 5, just after the 4. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10.
Which graph shows the solution to 12x−4<56 ? Select 1, 2, 3, or 4 for your answer.
Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items
Question
Use the image to answer the question.
Four number lines are shown labeled from 1 to 4 vertically one below the other. The number lines range from negative 10 to 10 with numbers listed in unit increments. The first number line has a closed point marked on 5. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10. The second number line has an open point marked on 5. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10. The third number line has a closed point plotted on the number line between 4 and 5, just after the 4. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10. The fourth number line has an open point plotted on the number line between 4 and 5, just after the 4. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10.
Which graph shows the solution to 12x−4<56 ? Select 1, 2, 3, or 4 for your answer.
To determine which graph shows the solution to 12x - 4 < 56, we need to analyze the given options and find the one that represents the correct inequality.
The inequality states that 12x - 4 is less than 56. To find the solution, we can isolate x by adding 4 to both sides of the inequality:
12x - 4 + 4 < 56 + 4
This simplifies to:
12x < 60
Now, divide both sides of the inequality by 12:
(12x)/12 < 60/12
This simplifies to:
x < 5
The correct graph should show a solution where x is less than 5.
Looking at the options, the only graph that satisfies this condition is graph number 4. Therefore, the correct answer is 4.
The inequality states that 12x - 4 is less than 56. To find the solution, we can isolate x by adding 4 to both sides of the inequality:
12x - 4 + 4 < 56 + 4
This simplifies to:
12x < 60
Now, divide both sides of the inequality by 12:
(12x)/12 < 60/12
This simplifies to:
x < 5
The correct graph should show a solution where x is less than 5.
Looking at the options, the only graph that satisfies this condition is graph number 4. Therefore, the correct answer is 4.
it was 2
Apologies for the confusion. If the correct answer is 2, then graph number 2 would show the solution to the inequality 12x - 4 < 56.