Which graph shows the solution of 9 - c < 2or - 3c > 15
(1 point)
To represent the solution of the inequality 9 - c < 2 or -3c > 15, we need to represent the solution to both inequalities on a number line.
For the first inequality, 9 - c < 2, we can start by subtracting 9 from both sides:
-c < 2 - 9.
Simplifying further, we have:
-c < -7.
To remove the negative sign, we need to divide both sides by -1. However, when you divide or multiply an inequality by a negative number, you need to switch the inequality sign. Therefore, we have:
c > 7.
The solution to the first inequality is c > 7.
Next, for the second inequality, -3c > 15, we can divide both sides by -3. We have to switch the inequality sign again because we're dividing by a negative number:
c < 15 / -3.
Simplifying further, we have:
c < -5.
The solution to the second inequality is c < -5.
To represent both solutions on a number line, we can draw an open circle at 7 to indicate that c is greater than the value, and an open circle at -5 to indicate that c is less than the value. Then, we can draw an arrow pointing to the right from the circle at 7 to indicate that c is greater than 7, and an arrow pointing to the left from the circle at -5 to indicate that c is less than -5.
The graph that represents the solution of the inequality 9 - c < 2 or -3c > 15 would look like this:
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To determine which graph shows the solution of 9 - c < 2 or -3c > 15, we need to solve each inequality separately and then graph the solutions.
First, let's solve the inequality 9 - c < 2:
9 - c < 2
Subtract 9 from both sides:
-c < -7
Multiply both sides by -1 (since we are multiplying by a negative number, the inequality sign flips):
c > 7
So the solution to the first inequality is c > 7.
Now, let's solve the inequality -3c > 15:
-3c > 15
Divide both sides by -3 (remember to flip the inequality sign when dividing by a negative number):
c < -5
So the solution to the second inequality is c < -5.
Now, we need to graph the solutions on the number line. The graph that represents c > 7 would have an open circle at 7 and an arrow pointing towards positive infinity (to the right). The graph that represents c < -5 would have an open circle at -5 and an arrow pointing towards negative infinity (to the left).
Here is a verbal description of the graph that shows the solution:
- Start with a number line.
- Plot an open circle at 7 and label it ">" to represent c > 7.
- Plot an open circle at -5 and label it "<" to represent c < -5.
- Draw an arrow starting from the open circle at 7 towards positive infinity (to the right).
- Draw an arrow starting from the open circle at -5 towards negative infinity (to the left).
Unfortunately, I cannot provide an actual graph as I am a text-based AI and do not have the capability to draw graphs.
To solve the inequality 9 - c < 2 or -3c > 15, we need to solve each inequality separately and then combine the solutions.
First, let's solve the inequality 9 - c < 2:
To isolate the variable, we can subtract 9 from both sides:
9 - c - 9 < 2 - 9
-c < -7
Next, we need to get c by itself, so we divide both sides of the inequality by -1. Remember, when we divide an inequality by a negative number, we need to reverse the inequality sign:
-c / -1 > -7 / -1
c > 7
So the solution to the first inequality is c > 7.
Next, let's solve the inequality -3c > 15:
To isolate the variable, we can divide both sides of the inequality by -3. Remember, when we divide an inequality by a negative number, we need to reverse the inequality sign:
-3c / -3 < 15 / -3
c < -5
So the solution to the second inequality is c < -5.
Now, let's plot the solutions to both inequalities on a number line:
On the number line, we mark a point at c = 7 and draw an open circle to indicate that it is not included in the solution.
Then, we mark a point at c = -5 and draw an open circle again.
Finally, we shade the region between the two points to show that the solutions to both inequalities are valid.
The resulting graph should have an open circle at 7, an open circle at -5, and a shaded region between them.