Solve the inequality. Graph and check your solutions.
y - 2 > - 17
To solve the inequality, we can add 2 to both sides of the inequality:
y - 2 + 2 > -17 + 2
y > -15
To graph the solution, we can draw a number line and mark the point -15 as a dashed line (since y is greater than -15) and shade the region to the right of -15:
--------------------------o---->
-20 -19 -18 -17 -16 -15 -14 -13 -12 -11
Now, to check our solution, we can choose a value on the shaded region, such as y = -10. Plugging this value into the original inequality:
-10 - 2 > -17
-12 > -17
Since -12 is indeed greater than -17, our solution is correct.
Therefore, the solution to the inequality y - 2 > -17 is y > -15.
To solve the inequality y - 2 > -17, we need to isolate the variable y on one side of the inequality symbol. Here's how we do it:
1. Add 2 to both sides of the inequality:
y - 2 + 2 > -17 + 2
Simplifying, we get:
y > -15
The solution is y > -15, meaning that any value of y that is greater than -15 will satisfy the inequality.
To graph the solution, we can represent it on a number line. We draw an open circle at -15 and shade the line to the right of that point, indicating that any value greater than -15 is a solution.
To check our solution, we can substitute a value greater than -15 into the original inequality and see if it holds true. For example, let's choose y = -10:
y - 2 > -17
-10 - 2 > -17
-12 > -17
Since -12 is indeed greater than -17, the inequality holds true.
To solve the inequality y - 2 > -17, we need to isolate the variable y.
Step 1: Add 2 to both sides of the inequality:
y - 2 + 2 > -17 + 2
y > -15
So, the solution to the inequality is y > -15.
To graph the solution, we will represent y on the vertical axis and -15 on the horizontal axis. We will use an open circle (>) to indicate that y is greater than -15.
Next, we can check the solution by substituting a number greater than -15 into the original inequality. Let's choose y = 0.
0 - 2 > -17
-2 > -17
Since -2 is indeed greater than -17, the inequality holds true when y = 0. Therefore, the solution is valid.