Solve the following inequality. Graph and check your solution.

Question

negative 15 less than minus 3 c
Question content area bottom
Part 1
Solve the inequality.
  
enter your response here
​(Simplify your answer. Type an​ inequality.)

Answer 1

To solve the inequality \( -15 < -3c \), we need to isolate \( c \).

1. Start with the original inequality: \[ -15 < -3c \]

2. To isolate \( c \), divide both sides by \(-3\). Remember that dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign: \[ \frac{-15}{-3} > c \] This simplifies to: \[ 5 > c \]

3. This can be rewritten as: \[ c < 5 \]

Solution

The solution to the inequality is: \[ c < 5 \]

Graphing the Solution

To graph the inequality \( c < 5 \):

• Draw a number line.
• Place an open circle on the number \( 5 \) to indicate that \( 5 \) is not included in the solution set.
• Shade to the left of \( 5 \) to indicate all numbers less than \( 5 \).

Checking the Solution

To verify the solution, we can test points:

• For \( c = 4 \), check the original inequality: \[ -15 < -3(4) \quad \Rightarrow \quad -15 < -12 \quad \text{(true)} \]
• For \( c = 6 \), check the original inequality: \[ -15 < -3(6) \quad \Rightarrow \quad -15 < -18 \quad \text{(false)} \]

This confirms that \( c < 5 \) is indeed the correct solution.