Question

Solve the inequality. Graph and check your solutions.

y−2>−20

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.

Answer 2

Solve the inequality. Graph and check your solutions.

−12≥y−4

Answer 3

[AI-generated answer — Bot GPT 3.5]

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.

Answer 4

Solve the inequality. Graph and check your solutions.

y−2>−

Answer 5

[AI-generated answer — Bot GPT 3.5]

It seems like you haven't provided the inequality completely. Could you please provide the complete inequality?

Answer 6

Solve the inequality. Graph and check your solutions.

y−2>−16

Answer 7

[AI-generated answer — Bot GPT 3.5]

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.

Answer 8

-5/6 <r -5/6

Answer 9

[AI-generated answer — Bot GPT 3.5]

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.

Answer 10

-2/5 ≥r -2/5

Answer 11

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we can add 2/5 to both sides:

-2/5 + 2/5 ≥ r - 2/5 + 2/5

This simplifies to:

0 ≥ r

In other words, r is less than or equal to 0.

To graph this inequality on a number line, we shade in the values that are less than or equal to 0:

|
---------|---------|---------
-2/5 0 2

All values to the left of 0 on the number line will be shaded, including 0.

To check our solutions, we can pick a few values less than or equal to 0 and substitute them into the original inequality to see if they satisfy the inequality.

For example, let's test the value r = -3:

-2/5 ≥ -3 - 2/5 ?

-2/5 ≥ -15/5 - This is true, so r = -3 is a solution to the inequality.

Another example could be r = 0:

-2/5 ≥ 0 - 2/5?

-2/5 ≥ -2/5 - This is also true, so r = 0 is a solution to the inequality.

Therefore, any value of r less than or equal to 0 satisfies the inequality.

Answer 12

Solve the inequality. Graph and check your solutions.

4/5+a>−6/5

Answer 13

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we can subtract 4/5 from both sides of the inequality:

4/5 + a - 4/5 > -6/5 - 4/5

This simplifies to:

a > -10/5

Simplifying further, we get:

a > -2

To graph this inequality, we draw a number line and shade in the values that are greater than -2:

|
----|---------|---------|----
-4 -2 0

All values greater than -2 on the number line will be shaded.

To check our solutions, we can pick a few values larger than -2 and substitute them into the original inequality to see if they satisfy the inequality.

For example, let's test the value a = 0:

4/5 + 0 > -6/5 ?

4/5 > -6/5 - This is true, so a = 0 is a solution to the inequality.

Another example could be a = 5:

4/5 + 5 > -6/5 ?

25/5 > -6/5 - This is also true, so a = 5 is a solution to the inequality.

Therefore, any value of a greater than -2 satisfies the inequality.

Answer 14

4/3≤n+3

Answer 15

[AI-generated answer — Bot GPT 3.5]

To solve this inequality, we can subtract 3 from both sides of the inequality:

4/3 - 3 ≤ n + 3 - 3

This simplifies to:

-7/3 ≤ n

To graph this inequality on a number line, we shade in the values that are greater than or equal to -7/3:

|
---------|---------|---------|---------
-7/3 0 3

All values to the right of -7/3 on the number line will be shaded, including -7/3.

To check our solutions, we can pick a few values greater than or equal to -7/3 and substitute them into the original inequality to see if they satisfy the inequality.

For example, let's test the value n = 0:

4/3 ≤ 0 + 3 ?

4/3 ≤ 3 - This is true, so n = 0 is a solution to the inequality.

Another example could be n = 2:

4/3 ≤ 2 + 3 ?

4/3 ≤ 5 - This is also true, so n = 2 is a solution to the inequality.

Therefore, any value of n greater than or equal to -7/3 satisfies the inequality.