Solve the following inequality. Graph and check your solution.
-12 < - 6c
To solve the given inequality, we will first isolate the variable c.
-12 < -6c
To do this, we divide both sides of the inequality by -6. However, since we are dividing by a negative number, the inequality sign flips.
-12/-6 > -6c/-6
2 > c
So, the solution to the inequality is c > 2.
To graph the solution, we plot a circle at 2 on the number line and shade the region to the right of 2.
To check the solution, we can choose a value greater than 2 and substitute it back in the inequality. Let's choose 3.
-12 < -6(3)
-12 < -18
Since -12 is indeed less than -18, our solution of c > 2 holds true.
Therefore, the solution to the inequality -12 < -6c is c > 2.
To solve the inequality -12 < -6c, we need to isolate the variable c.
Step 1: Divide both sides of the inequality by -6. Keep in mind that dividing by a negative number flips the direction of the inequality.
Since we divide both sides of the inequality by -6, we have:
(-12) / (-6) > c
Simplifying this, we get:
2 > c
So the solution to the inequality is c < 2.
To graph and check the solution, we can plot a number line and shade the area where c is less than 2.
-∞------------2-------------∞
Since the inequality is not inclusive (strict inequality), we leave an open circle at 2 to indicate that it is not included. Then we shade to the left of 2 to represent all the values of c that are less than 2.
To check the solution, we can choose a value that is less than 2, such as 1. Plugging it back into the original inequality:
-12 < -6(1)
-12 < -6
This is true, so our solution is valid.
To solve the inequality -12 < -6c, we need to isolate the variable c.
Step 1: Divide both sides of the inequality by -6. Remember that when we divide an inequality by a negative number, the direction of the inequality sign changes.
-12 / -6 > -6c / -6
Simplifying, we get:
2 > c
Step 2: Now we can graph the solution. To do this, we draw a number line and mark the point where c is 2. Since the inequality is greater than, we use an open circle to represent the point.
```
<------(o)=====[=================]------->
2 -1 0 1 2
```
Step 3: Finally, we need to check our solution to ensure its accuracy. We can choose a number in the inequality, such as 1, and see if it satisfies the inequality.
Plugging in c = 1 into the original inequality:
-12 < -6(1)
-12 < -6
Since -12 is indeed less than -6, our solution is correct.
Therefore, the solution to the inequality -12 < -6c is c > 2, which can also be expressed as c ∈ (2, ∞).