Question

solve the inequality and graph the solution.
12 + 2n > 8
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 12 from both sides

To isolate the term with \( n \), we subtract 12 from both sides of the inequality \( 12 + 2n > 8 \). This gives us \( 12 + 2n - 12 > 8 - 12 \), which simplifies to \( 2n > -4 \).

Step2: Divide by 2

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

Step3: Graph the solution

On the number line, we plot an open circle at \( -2 \) (since the inequality is \( > \), not \( \geq \)) and draw an arrow to the right to represent all numbers greater than \( -2 \).

Answer:

The solution to the inequality \( 12 + 2n > 8 \) is \( n > -2 \). The graph has an open circle at \( -2 \) and an arrow pointing to the right.