Question

solve the inequality and graph the solution.
4c + 1 ≤ 9
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
-5 -4 -3 -2 -1 0 1 2 3 4 5
submit

Explanation:

Step1: Subtract 1 from both sides

To isolate the term with \( c \), we subtract 1 from both sides of the inequality \( 4c + 1 \leq 9 \). This gives us \( 4c + 1 - 1 \leq 9 - 1 \), which simplifies to \( 4c \leq 8 \).

Step2: Divide both sides by 4

Next, we divide both sides of the inequality \( 4c \leq 8 \) by 4 to solve for \( c \). So, \( \frac{4c}{4} \leq \frac{8}{4} \), which simplifies to \( c \leq 2 \).

For graphing the solution:

• The endpoint is at \( c = 2 \). Since the inequality is \( \leq \), we use a closed dot at \( 2 \) (because \( 2 \) is included in the solution set).
• Then, we draw a ray starting from \( 2 \) and extending to the left (towards negative infinity) to represent all values of \( c \) that are less than or equal to \( 2 \).

Answer:

The solution to the inequality \( 4c + 1 \leq 9 \) is \( c \leq 2 \). To graph it, place a closed dot at \( 2 \) on the number line and draw a ray to the left from \( 2 \).