Match the inequality to the graph of its solution.(2 points)
C+7<3
C+7<3
C-3<1
C-3<1
C-7<3
Sorry, but I can't generate a visualization for you as I am a text-based AI model. However, I can help you understand how to determine the solution to each inequality.
For the first inequality, C + 7 < 3, we can solve it by subtracting 7 from both sides: C < 3 - 7, which simplifies to C < -4. The solution to this inequality is all values of C that are less than -4.
For the second inequality, C - 3 < 1, we can solve it by adding 3 to both sides: C < 1 + 3, which simplifies to C < 4. The solution to this inequality is all values of C that are less than 4.
For the third inequality, C - 7 < 3, we can solve it by adding 7 to both sides: C < 3 + 7, which simplifies to C < 10. The solution to this inequality is all values of C that are less than 10.
So, the solutions to the three inequalities are:
1. C < -4
2. C < 4
3. C < 10
I hope this clarifies things for you!
To match the inequality to the graph of its solution, we need to first solve each inequality for C and then plot the solutions on a number line.
1. C + 7 < 3:
To solve this inequality, we subtract 7 from both sides:
C + 7 - 7 < 3 - 7
C < -4
The solution to this inequality is C < -4. On the number line, we would draw an open circle at -4 and shade to the left of it, representing all values of C that are less than -4.
2. C - 3 < 1:
To solve this inequality, we add 3 to both sides:
C - 3 + 3 < 1 + 3
C < 4
The solution to this inequality is C < 4. On the number line, we would draw an open circle at 4 and shade to the left of it, representing all values of C that are less than 4.
3. C - 7 < 3:
To solve this inequality, we add 7 to both sides:
C - 7 + 7 < 3 + 7
C < 10
The solution to this inequality is C < 10. On the number line, we would draw an open circle at 10 and shade to the left of it, representing all values of C that are less than 10.
Now, let's match the inequalities to their corresponding graphs:
1. C + 7 < 3 matches the graph with shading to the left of an open circle at -4.
2. C - 3 < 1 matches the graph with shading to the left of an open circle at 4.
3. C - 7 < 3 matches the graph with shading to the left of an open circle at 10.
To match the inequality to the graph of its solution, we need to understand how inequalities relate to the number line.
Let's focus on the first inequality, C + 7 < 3. To solve this inequality, we need to isolate C on one side of the equation.
Step 1: Subtract 7 from both sides of the inequality:
C + 7 - 7 < 3 - 7
C < -4
Now we have C < -4, which means C is less than -4. To graph this inequality on the number line, we represent the solution as a shaded region:
---(-∞)----(-4)---·-----(∞)---
The shaded region extends to the left of -4, indicating that any value of C less than -4 satisfies the inequality C + 7 < 3.
Now, let's move on to the second inequality, C - 3 < 1.
Step 1: Add 3 to both sides of the inequality:
C - 3 + 3 < 1 + 3
C < 4
The solution to C - 3 < 1 is C < 4, which means C is less than 4. On the number line, we represent this as:
---(-∞)----4---·-----(∞)---
The shaded region is to the left of 4, indicating that any value of C less than 4 satisfies the inequality C - 3 < 1.
Finally, let's consider the third inequality, C - 7 < 3.
Step 1: Add 7 to both sides of the inequality:
C - 7 + 7 < 3 + 7
C < 10
The solution to C - 7 < 3 is C < 10, which means C is less than 10. On the number line, we represent this as:
---(-∞)----10---·-----(∞)---
The shaded region is to the left of 10, indicating that any value of C less than 10 satisfies the inequality C - 7 < 3.
To summarize the solutions on the corresponding graph:
1. C + 7 < 3 -> Solution: C < -4 -> Graph: ---(-∞)----(-4)---·-----(∞)---
2. C - 3 < 1 -> Solution: C < 4 -> Graph: ---(-∞)----4---·-----(∞)---
3. C - 7 < 3 -> Solution: C < 10 -> Graph: ---(-∞)----10---·-----(∞)---
2.7 ≤ b + 5
(1 point)
Responses
b ≥ 7.7
b ≥ 7.7
b ≥ –2.3
b ≥ –2.3
b ≤ 2.3
b ≤ 2.3
b ≤ –7.7
To solve the inequality 2.7 ≤ b + 5, we need to isolate b on one side of the inequality.
Step 1: Subtract 5 from both sides of the inequality:
2.7 - 5 ≤ b + 5 - 5
-2.3 ≤ b
The solution to the inequality is -2.3 ≤ b. This means that b is greater than or equal to -2.3. On the number line, we represent this as:
---(-∞)----(-2.3)---·-----(∞)---
The shaded region extends to the right of -2.3, indicating that any value of b greater than or equal to -2.3 satisfies the inequality 2.7 ≤ b + 5.
So, the matching response for the inequality 2.7 ≤ b + 5 is:
b ≥ -2.3.
You have a gift card for your favorite clothing store for the amount of $60. You have found a shirt you want to buy that costs $15. If you don't want to spend more than the amount of the gift card, which of the following inequalities could be used to determine the amount you have left to spend?
(1 point)
Responses
x + 15 ≥ 60
x + 15 ≥ 60
x – 15 ≥ 60
x – 15 ≥ 60
x – 15 ≤ 60
x – 15 ≤ 60
x + 15 ≤ 60
x + 15 ≤ 60
To determine the amount you have left to spend, we need to subtract the cost of the shirt ($15) from the amount of the gift card ($60).
Let x represent the amount you have left to spend.
The correct inequality that represents the amount you have left to spend is:
x - 15 ≤ 60
This is because you want to make sure that the amount you have left to spend (x) is less than or equal to the remaining balance of the gift card ($60).
So, the matching response for the given scenario is:
x - 15 ≤ 60.