Question

solve the inequality ( y - 8 > -6 ).
( y - 8 > -6 )
( +8 +8 ) add 8 on both sides.
( y > 2 )
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.

Explanation:

Step1: Add 8 to both sides

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

Step2: Simplify

$$y>2$$

To graph \(y > 2\) on the number line:

• Place an open circle at \(y = 2\) (because \(2\) is not included in the solution set, as the inequality is \(>\) not \(\geq\)).
• Shade the region to the right of \(2\) on the number line.

Answer:

The solution of the inequality \(y-8 > - 6\) is \(y>2\). On the number - line, there is an open circle at \(2\) and the line is shaded to the right of \(2\).