Solve the inequality. Graph and check your solutions.
y−2>−20
To solve the inequality, we can add 2 to both sides of the inequality:
y - 2 + 2 > -20 + 2
This simplifies to:
y > -18
To graph this inequality, we draw a number line and shade in the values that are greater than -18:
|
---------|---------|------------|----
-20 -18 0
All values to the right of -18 on the number line will be shaded.
To check our solutions, we can pick a few values greater than -18 and substitute them into the original inequality to see if they satisfy the inequality.
For example, let's test the value y = -17:
-17 - 2 > -20 ?
-19 > -20 - This is true, so -17 is a solution to the inequality.
Another example could be y = 0:
0 - 2 > -20 ?
-2 > -20 - This is true, so 0 is also a solution to the inequality.
Therefore, any value of y greater than -18 satisfies the inequality.
Solve the inequality. Graph and check your solutions.
−12≥y−4
To solve the inequality, we can first add 4 to both sides of the inequality:
-12 + 4 ≥ y - 4 + 4
This simplifies to:
-8 ≥ y
To graph this inequality, we draw a number line and shade in the values that are less than or equal to -8:
|
---------|---------|---------|---------
-12 -8 0
All values to the left of -8 on the number line will be shaded, including -8.
To check our solutions, we can pick a few values less than or equal to -8 and substitute them into the original inequality to see if they satisfy the inequality.
For example, let's test the value y = -9:
-12 ≥ -9 - 4 ?
-12 ≥ -13 - This is true, so -9 is a solution to the inequality.
Another example could be y = -8:
-12 ≥ -8 - 4 ?
-12 ≥ -12 - This is also true, so -8 is a solution to the inequality.
Therefore, any value of y less than or equal to -8 satisfies the inequality.
Solve the inequality. Graph and check your solutions.
y−2>−
It seems like you haven't provided the inequality completely. Could you please provide the complete inequality?
Solve the inequality. Graph and check your solutions.
y−2>−16
To solve the inequality, we can add 2 to both sides of the inequality:
y - 2 + 2 > -16 + 2
This simplifies to:
y > -14
To graph this inequality, we draw a number line and shade in the values that are greater than -14:
|
---------|---------|----------|----
-16 -14 0
All values to the right of -14 on the number line will be shaded.
To check our solutions, we can pick a few values greater than -14 and substitute them into the original inequality to see if they satisfy the inequality.
For example, let's test the value y = -10:
-10 - 2 > -16 ?
-12 > -16 - This is true, so -10 is a solution to the inequality.
Another example could be y = -5:
-5 - 2 > -16 ?
-7 > -16 - This is also true, so -5 is a solution to the inequality.
Therefore, any value of y greater than -14 satisfies the inequality.
-5/6 <r -5/6
To solve the inequality, we can add 5/6 to both sides of the inequality:
-5/6 + 5/6 < r - 5/6 + 5/6
This simplifies to:
0 < r
To graph this inequality, we draw a number line and shade in the values that are greater than 0:
|
----|---------|---------|----
-2 0 2
All values to the right of 0 on the number line will be shaded.
To check our solutions, we can pick a few values greater than 0 and substitute them into the original inequality to see if they satisfy the inequality.
For example, let's test the value r = 1:
-5/6 < 1 - 5/6?
-5/6 < 1/6 - This is true, so r = 1 is a solution to the inequality.
Another example could be r = 5:
-5/6 < 5 - 5/6?
-5/6 < 25/6 - This is also true, so r = 5 is a solution to the inequality.
Therefore, any value of r greater than 0 satisfies the inequality.