Question

solve the inequality and graph the solution.
-8 > 4 + 3c
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.
-5 -4 -3 -2 -1 0 1 2 3 4 5

Explanation:

Step1: Subtract 4 from both sides

To isolate the term with \( c \), we subtract 4 from both sides of the inequality \(-8 > 4 + 3c\). This gives \(-8 - 4>4 + 3c- 4\), which simplifies to \(-12>3c\).

Step2: Divide by 3

Next, we divide both sides of the inequality \(-12>3c\) by 3 to solve for \( c \). So, \(\frac{-12}{3}>\frac{3c}{3}\), which simplifies to \(-4 > c\) (or \(c < - 4\)).

Step3: Graph the solution

For the inequality \(c < - 4\), we use an open circle at \(-4\) (since \(c\) is not equal to \(-4\)) and draw an arrow to the left (because we want all values less than \(-4\)).

Answer:

The solution to the inequality is \(c < - 4\). The graph has an open circle at \(-4\) and an arrow pointing to the left along the number line.