How many whole numbers less than 10 are solutions of 4x−8≤4?(1 point)
The correct answer is:
0, 1, 2, 3
To solve the inequality 4x - 8 ≤ 4, we can add 8 to both sides:
4x - 8 + 8 ≤ 4 + 8
4x ≤ 12
Then, we can divide both sides by 4:
4x/4 ≤ 12/4
x ≤ 3
So, the solutions of the inequality are all the whole numbers less than or equal to 3. Since we are looking for whole numbers less than 10, we only need to consider the numbers 0, 1, 2, and 3. Therefore, there are 4 solutions.
Which whole numbers less than 10 are solutions of 4x−8≤4?(1 point)
Responses
1, 2, 3, 4
0, 1, 2, 3
0, 2, 4, 6
1, 2, 3, 5
Which of the numbers 1, 2, and 3 is a solution of 2x+1≥7?(1 point)
Which symbol in place of the question mark makes the inequality 2x ? 20 true for the solutions 10, 11, and 12?
To find out which symbol in place of the question mark makes the inequality 2x ? 20 true for the solutions 10, 11, and 12, we can substitute each number for x and see which symbols make the inequality true.
For x = 10, we have:
2(10) ? 20
20 ? 20
This is not true for any symbol, because 20 is not less than, greater than, or equal to 20.
For x = 11, we have:
2(11) ? 20
22 ? 20
This is true if we use the greater than symbol, so:
2x > 20
For x = 12, we have:
2(12) ? 20
24 ? 20
This is also true if we use the greater than symbol.
Therefore, the answer is:
>
What number is not part of the solution set for z/5≠7?
To solve the inequality z/5 ≠ 7, we can multiply both sides by 5:
z ≠ 7 x 5
z ≠ 35
So, any number that is not 35 is part of the solution set. Therefore, the number that is not part of the solution set is:
35
What is the solution to the inequality h+8≤9+12? Include the appropriate inequality symbol in your response. (1 point)
To solve the inequality h + 8 ≤ 9 + 12, we can simplify the right side:
h + 8 ≤ 9 + 12
h + 8 ≤ 21
Then, we can subtract 8 from both sides:
h + 8 - 8 ≤ 21 - 8
h ≤ 13
The solution is:
h ≤ 13
Therefore, the appropriate inequality symbol to include in the response is:
≤
What is the solution to the inequality h+8≤9+12?
To solve the inequality h + 8 ≤ 9 + 12, we can simplify the right side:
h + 8 ≤ 9 + 12
h + 8 ≤ 21
Then, we can subtract 8 from both sides:
h + 8 - 8 ≤ 21 - 8
h ≤ 13
The solution is:
h ≤ 13
Sherri’s bakery has sold 75 bagels. She needs to sell at least 450 bagels to make a profit for the day. What is the solution of an inequality showing the number of bagels (b) that she still needs to sell
Let b be the number of bagels Sherri still needs to sell to make a profit for the day. We can write an inequality to represent this situation as:
75 + b ≥ 450
The left side of the inequality represents the number of bagels Sherri has sold so far (75) plus the number of bagels she still needs to sell (b), which must be greater than or equal to the total number of bagels she needs to sell (450) to make a profit.
To solve for b, we can subtract 75 from both sides of the inequality:
b ≥ 450 - 75
b ≥ 375
Therefore, the solution of the inequality showing the number of bagels (b) that Sherri still needs to sell is:
b ≥ 375
To avoid drowsiness and complaints of stale air, the amount of carbon dioxide (CO2) in a workplace must not be greater than 1,000 parts per million (ppm). How would you write an inequality to show the amount of (CO2) in parts per million that would cause drowsiness and complaints of stale air?
To write an inequality to show the amount of carbon dioxide (CO2) in parts per million (ppm) that would cause drowsiness and complaints of stale air, we can use the symbol ≤ (less than or equal to) because the amount of CO2 must not be greater than 1,000 ppm.
So, the inequality would be:
CO2 ≤ 1,000 ppm
This inequality means that the amount of CO2 in the workplace must be less than or equal to 1,000 ppm in order to avoid drowsiness and complaints of stale air.
Which of the numbers 1, 2, and 3 is a solution of 2x+1≥7
To find out which of the numbers 1, 2, and 3 is a solution of the inequality 2x + 1 ≥ 7, we can substitute each number for x and see which ones make the inequality true.
For x = 1, we have:
2(1) + 1 ≥ 7
2 + 1 ≥ 7
3 ≥ 7
This is not true, so 1 is not a solution.
For x = 2, we have:
2(2) + 1 ≥ 7
4 + 1 ≥ 7
5 ≥ 7
This is not true, so 2 is not a solution.
For x = 3, we have:
2(3) + 1 ≥ 7
6 + 1 ≥ 7
7 ≥ 7
This is true, so 3 is a solution.
Therefore, the answer is:
3
Which symbol in place of the question mark makes the inequality 2x ? 20 true for the solutions 10, 11, and 12?
To find out which symbol in place of the question mark makes the inequality 2x ? 20 true for the solutions 10, 11, and 12, we can substitute each number for x and see which symbols make the inequality true.
For x = 10, we have:
2(10) ? 20
20 ? 20
This is not true for any symbol, because 20 is not less than, greater than, or equal to 20.
For x = 11, we have:
2(11) ? 20
22 ? 20
This is true if we use the greater than symbol, so:
2x > 20
For x = 12, we have:
2(12) ? 20
24 ? 20
This is also true if we use the greater than symbol.
Therefore, the answer is:
>
What number is not part of the solution set for z5≠7
There seems to be a typo in the inequality provided.
Assuming the inequality should be z/5 ≠ 7, the solution would be:
To solve the inequality z/5 ≠ 7, we can multiply both sides by 5:
z/5 ≠ 7
z ≠ 7 * 5
z ≠ 35
So, any number that is not 35 is part of the solution set. Therefore, the number that is not part of the solution set is:
35
If the representation of an inequality on a number line features a hollow circle with an arrow pointing leftward, what symbol would be used in the inequality itself?
The hollow circle on a number line represents that the endpoint itself is not included in the solution set. The arrow pointing leftward indicates that the solution set includes all numbers to the left of the endpoint.
The symbol used in the inequality itself would be:
< (less than)
For example, if the endpoint is labeled as "a", and the arrow points leftward, the inequality would be:
x < a
This inequality means that the solution set includes all values of x that are less than a, but does not include the value of a itself.
Which statement is true about the number of solutions to an inequality?
The statement that is true about the number of solutions to an inequality is:
An inequality may have zero, one, or infinitely many solutions.
The number of solutions to an inequality can vary depending on the values of the variables and the nature of the inequality. Some inequalities may have no solutions, meaning that there is no valid value of the variable that satisfies the inequality. Others may have a single solution, meaning that there is only one value of the variable that satisfies the inequality. And still others may have infinitely many solutions, meaning that there are many possible values of the variable that satisfy the inequality.
For example, the inequality x > 5 has infinitely many solutions, because any value of x greater than 5 would satisfy the inequality. On the other hand, the inequality x < 0 has no solutions, because there is no value of x less than 0. And the inequality x = 3 has only one solution, because x can only equal 3 and no other value would make the inequality true.
An inequality using any of the inequality symbols has an infinite number of solutions. An inequality using all but one of the inequality symbols also has an infinite number of nonsolutions. Which inequality symbol produces an inequality with a finite number of nonsolutions?
The inequality symbol that produces an inequality with a finite number of nonsolutions is:
= (equal to)
An inequality using the equal to symbol, x = 5 for instance, has only one solution, which is x = 5. All other values of x are not solutions to this inequality, meaning that it has a finite number of nonsolutions.
Inequalities using other symbols such as < (less than), ≤ (less than or equal to), > (greater than), ≥ (greater than or equal to), and ≠ (not equal to) can have infinite solutions or infinite nonsolutions, depending on the nature of the inequality and the variables involved.
To avoid drowsiness and complaints of stale air, the amount of carbon dioxide (CO2) in a workplace must not be greater than 1,000 parts per million (ppm). How would you write an inequality to show the amount of (CO2) in parts per million that would cause drowsiness and complaints of stale air?
To write an inequality representing the maximum amount of carbon dioxide (CO2) in parts per million (ppm) that would cause drowsiness and complaints of stale air as 1,000 ppm, we can use the symbol ≤ (less than or equal to), because the amount of CO2 must not be greater than 1,000 ppm.
So, the inequality would be:
CO2 ≤ 1,000 ppm
This inequality means that the amount of CO2 in the workplace must be less than or equal to 1,000 ppm in order to avoid drowsiness and complaints of stale air.
What is the solution to the inequality h+8≤9+12? Include the appropriate inequality symbol in your response.
To solve the inequality h + 8 ≤ 9 + 12, we can simplify the right side:
h + 8 ≤ 9 + 12
h + 8 ≤ 21
Then, we can subtract 8 from both sides:
h + 8 - 8 ≤ 21 - 8
h ≤ 13
The solution is:
h ≤ 13
Therefore, the appropriate inequality symbol to include in the response is:
≤
So, the complete solution to the inequality is:
h + 8 ≤ 9 + 12
h ≤ 13
Sherri’s bakery has sold 75 bagels. She needs to sell at least 450 bagels to make a profit for the day. What is the solution of an inequality showing the number of bagels (b) that she still needs to sell? Include the appropriate inequality symbol in your response.
Let b be the number of bagels Sherri still needs to sell to make a profit for the day. We can write an inequality to represent this situation as:
75 + b ≥ 450
The left side of the inequality represents the number of bagels Sherri has sold so far (75) plus the number of bagels she still needs to sell (b), which must be greater than or equal to the total number of bagels she needs to sell (450) to make a profit.
To solve for b, we can subtract 75 from both sides of the inequality:
b ≥ 450 - 75
b ≥ 375
Therefore, the solution of the inequality showing the number of bagels (b) that Sherri still needs to sell is:
b ≥ 375
The appropriate inequality symbol to include in the response is:
≥ (greater than or equal to)
What is the solution of the inequality 7x≥56? Include the appropriate inequality symbol in your response.
To solve the inequality 7x ≥ 56, we can divide both sides by 7:
7x/7 ≥ 56/7
x ≥ 8
The solution is:
x ≥ 8
Therefore, the appropriate inequality symbol to include in the response is:
≥
So, the complete solution to the inequality is:
7x ≥ 56
x ≥ 8
What is the solution of the inequality p5≤8? Include the appropriate inequality symbol in your response.
To solve the inequality p/5 ≤ 8, we can multiply both sides by 5:
p/5 x 5 ≤ 8 x 5
p ≤ 40
The solution is:
p ≤ 40
Therefore, the appropriate inequality symbol to include in the response is:
≤
So, the complete solution to the inequality is:
p/5 ≤ 8
p ≤ 40
The 8 members of a band want to order matching T-shirts without spending more than $136. What is the solution of an inequality representing their situation? Use t for the cost of one shirt.
If the cost of one shirt is t, then the cost of 8 shirts will be 8t.
To represent the situation where the 8 members of a band want to order matching T-shirts without spending more than $136, we can use the inequality:
8t ≤ 136
The left side of the inequality represents the maximum amount of money the band can spend on the T-shirts (8t) and the right side represents the maximum amount they can spend ($136), which they must not exceed.
To solve for t, we can divide both sides by 8:
8t/8 ≤ 136/8
t ≤ 17
The solution is:
t ≤ 17
Therefore, the appropriate inequality symbol to include in the response is:
≤
So, the complete solution to the inequality is:
8t ≤ 136
t ≤ 17
How many suitcases averaging 25 pounds apiece can be loaded onto a plane that can hold a maximum of 1,750 pounds of storage? How would you write an inequality expressing this situation? Use s for the weight of one suitcase, and include it on the left side of the inequality. Do not solve the inequality.
Let s be the weight (in pounds) of one suitcase and let x be the number of suitcases.
To find the maximum number of suitcases that can be loaded onto a plane that can hold a maximum of 1,750 pounds of storage:
We can set up an inequality that relates the number of suitcases (x) and the weight of one suitcase (s) to the maximum weight that the plane can hold (1,750 pounds):
xs ≤ 1,750
This inequality means that the weight of x suitcases (xs) cannot exceed the maximum weight of the plane (1,750 pounds).
To optimize the number of suitcases that can be loaded, we can divide both sides of the inequality by s, which gives:
x ≤ 1,750 / s
This expression gives the maximum number of suitcases that can be loaded onto the plane, given the weight limit and assuming that each suitcase weighs s pounds.
Therefore, the inequality expressing the situation is:
xs ≤ 1,750
And the maximum number of suitcases (x) that can be loaded onto the plane is:
x ≤ 1,750 / s
Two rectangles are drawn with chalk. The first rectangle has a length of 1.5 meters and a width of 0.75 meters. The second rectangle has a length of 1.75 meters and a width of 0.5 meters. What is the difference between the area of the rectangles?
To find the area of the first rectangle, we can multiply the length and width:
Area of first rectangle = length x width = 1.5 m x 0.75 m = 1.125
4.4 x 11.5
what is 11.5 x 4.4 ?
To find out if 1, 2, or 3 is a solution of the inequality 2x + 1 ≥ 7, we can substitute each number for x and see which ones make the inequality true.
For x = 1, we have:
2(1) + 1 ≥ 7
2 + 1 ≥ 7
3 ≥ 7
This is not true, so 1 is not a solution.
For x = 2, we have:
2(2) + 1 ≥ 7
4 + 1 ≥ 7
5 ≥ 7
This is not true, so 2 is not a solution.
For x = 3, we have:
2(3) + 1 ≥ 7
6 + 1 ≥ 7
7 ≥ 7
This is true, so 3 is a solution.
Therefore, the answer is:
3