Solve. 9 - c < 2 or -3c > 15.
I think it's -c < 7 and -c < -5 . Would you the two arrows facing each other?
9 -c < 2
Subtract 9 from both sides.
-c < -7
When multiplying by negative number, the carat gets reversed.
c > 7
Repeat for second inequality. Multiply both sides by -1/3.
c < -5
9 - c < 2 ... adding c and subtracting 2 ... 7 < c
-3 c > 15 ... dividing by -3 ... c < -5
9 - c < 2 OR -3c > 15
-c < -7 OR -c > 5
c > 7 OR c < -5
On a number line, draw a line to the left with an arrow at its end starting at -5
and a line with an arrow at its end to the right of 7
Well, well, well, it seems we have some inequalities to solve here! Let's break it down together.
First off, we have 9 - c < 2. To solve this, we want to isolate the "c" on one side. So, let's subtract 9 from both sides: -c < -7. And as much as arrows facing each other can represent intense conversation, in this case we need a good ol' "less than" sign, so it turns out we have -c < -7.
Now, let's move on to the next one, -3c > 15. We perform the same operation here, dividing both sides by -3 (don't worry, dividing is the only thing that isn't divided on opinions): c < -5.
So, it seems we ended up with -c < -7 and c < -5. The first one doesn't give us any hints about the value of "c," but the second one implies that "c" has to be smaller than -5. So, yes, we can say that -c < 7 and -c < -5.
Hope that clears things up!
To solve the inequalities 9 - c < 2 and -3c > 15, we need to isolate the variable "c" on one side of the inequality sign. Let's solve each inequality separately:
1) 9 - c < 2:
To isolate "c," you can start by subtracting 9 from both sides of the inequality:
9 - c - 9 < 2 - 9
-c < -7
Since we multiplied or divided both sides of the inequality by a negative number (-1), we need to reverse the inequality sign:
c > 7
2) -3c > 15:
Start by dividing both sides of the inequality by -3. However, when dividing or multiplying both sides of an inequality by a negative number, we need to reverse the inequality sign:
-3c / -3 < 15 / -3
c < -5
So the solution to the system of inequalities is c < -5 or c > 7. We can represent this on a number line using two arrows facing away from each other: ⟵ -∞ ... -5 ⟶ 7 ⟵ +∞