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Part 1
Solve the following inequality. Graph and check your solution.
-16> -8c
To solve the inequality "-16 > -8c", we need to isolate the variable "c" on one side of the inequality sign.
Dividing both sides of the inequality by -8, we need to flip the inequality sign since we are dividing by a negative number:
-16 / -8 < -8c / -8
2 < c
So the solution to the inequality is c > 2.
Let's graph this inequality on a number line:
-------------------------------|---|---|---|---|---|---
-2 -1 0 1 2 3 4
-------------------------------|---|---|---|---|---|---
Any value to the right of 2 (not including 2 itself) satisfies the inequality.
To check our solution, we can plug in a few values for "c" and see if they make the inequality true.
For example, let's try c = 3:
-16 > -8(3)
-16 > -24
This is true, so c = 3 satisfies the inequality.
Now, let's try c = 1:
-16 > -8(1)
-16 > -8
This is not true, so c = 1 does not satisfy the inequality.
Therefore, our solution is correct: c > 2.
To solve the inequality -16 > -8c, we need to isolate the variable c. Let's start by dividing both sides of the inequality by -8:
-16 / -8 > c
This simplifies to:
2 > c
So the solution to the inequality is c < 2.
To graph this solution, we represent it on a number line. We draw an open circle at 2 (since c cannot be equal to 2), and shade the area to the left of 2. This indicates that any value of c less than 2 will satisfy the inequality.
Checking the solution:
Let's choose a number less than 2, such as c = 1. Plugging it into the original inequality:
-16 > -8(1)
-16 > -8
The inequality is true, so c = 1 is a valid solution.
To solve the inequality -16 > -8c, we need to isolate the variable c.
1. Start by dividing both sides of the inequality by -8 to get rid of the coefficient:
(-16) / (-8) > (-8c) / (-8)
2 > c
2. Now we have the solution c > 2. This means that any value of c greater than 2 will satisfy the inequality.
To graph the solution on a number line:
- Start by drawing a number line and marking a point at 2.
- Since c is greater than 2, shade the line to the right of 2 to show the solution.
Checking the solution:
- Let's choose a value for c that is greater than 2, such as c = 3.
- Substituting c = 3 into the original inequality, we get:
-16 > -8(3)
-16 > -24 <- this is true
- Since -16 is indeed greater than -24, the solution c > 2 is correct.