Question

solve the inequality and graph the solution.
6y - 2 > -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.
(number line with -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 marked)

Explanation:

Step1: Add 2 to both sides

To isolate the term with \( y \), we add 2 to both sides of the inequality \( 6y - 2 > -8 \). This gives us \( 6y - 2 + 2 > -8 + 2 \), which simplifies to \( 6y > -6 \).

Step2: Divide by 6

Next, we divide both sides of the inequality \( 6y > -6 \) by 6 to solve for \( y \). So, \( \frac{6y}{6} > \frac{-6}{6} \), which simplifies to \( y > -1 \).

Step3: Graph the solution

The solution \( y > -1 \) means we have an open circle at \( -1 \) (since the inequality is strict, \( y
eq -1 \)) and an arrow pointing to the right (because \( y \) is greater than \( -1 \)).

Answer:

The solution to the inequality \( 6y - 2 > -8 \) is \( y > -1 \). For the graph, place an open circle at \( -1 \) and draw an arrow to the right.