Question

solve the inequality $y - 8 > -6$.
$y - 8 > -6$
$\underline{\quad\quad\quad\quad\quad\quad\quad}$
$+8\quad\quad\quad+8$
$\underline{\quad\quad\quad\quad\quad\quad\quad}$
$y > 2$
add 8 on both sides.
3 is included in the solution set because it makes the inequality true.
2 and 1 are not included in the solution set because they make the inequality false.
graph the solution set of the inequality.
(number line from -10 to 10 with ticks at each integer, and some circle and dot symbols with arrows)

Explanation:

Step1: Isolate $y$ by adding 8 to both sides

$y - 8 + 8 > -6 + 8$

Step2: Simplify both sides of the inequality

$y > 2$

Step3: Verify solution validity

Test $y=3$: $3-8=-5 > -6$ (true, included). Test $y=2$: $2-8=-6$ which is not greater than $-6$ (false, excluded). Test $y=1$: $1-8=-7 > -6$ (false, excluded).

Step4: Graph the solution

Draw an open circle at $y=2$ on the number line, then shade all values to the right of 2.

Answer:

The solved inequality is $\boldsymbol{y > 2}$. For the graph: place an open circle at 2 on the number line, and shade the region to the right of 2. All values greater than 2 are included in the solution set.