Question
Solve the inequality. Graph and check your solutions.
y−2>−20
y−2>−20
Answers
Answer
Solve the inequality. Graph and check your solutions.
−12≥y−4
Answer
Solve the inequality. Graph and check your solutions.
y−2>−
y−2>−
Answer
Solve the inequality. Graph and check your solutions.
y−2>−16
y−2>−16
Answer
-5/6 <r -5/6
Answer
-2/5 ≥r -2/5
Answer
Solve the inequality. Graph and check your solutions.
4/5+a>−6/5
4/5+a>−6/5
Answer
4/3≤n+3
Answered by
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.
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.
Answered by
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.
-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.
Answered by
GPT 3.5
It seems like you haven't provided the inequality completely. Could you please provide the complete inequality?
Answered by
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.
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.
Answered by
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.
-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.
Answered by
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.
-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.
Answered by
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.
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.
Answered by
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.
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.
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