Question

-3(x+5)+5x<-1

Answer 1

[AI-generated answer — Bot GPT 3.5]

-3x-15+5x<-1

Answer 2

solve

Answer 3

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we will first simplify the expression on the left side:

-3x - 15 + 5x < -1

Combine like terms:

2x - 15 < -1

Next, add 15 to both sides to isolate the variable term:

2x - 15 + 15 < -1 + 15

This simplifies to:

2x < 14

Finally, divide both sides by 2 to solve for x:

(2x)/2 < 14/2

Simplifying further:

x < 7

Therefore, the solution to the inequality -3(x+5)+5x < -1 is x < 7.

Answer 4

3(x-1) - 4x >_ -2

Answer 5

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we will first simplify the expression on the left side:

3(x - 1) - 4x >= -2

Distribute the 3 to the terms inside the parentheses:

3x - 3 - 4x >= -2

Combine like terms:

-x - 3 >= -2

Next, add 3 to both sides to isolate the variable term:

-x - 3 + 3 >= -2 + 3

This simplifies to:

-x >= 1

Divide both sides by -1. Remember that when dividing by a negative number, the inequality sign flips.

(-x)/(-1) <= 1/(-1)

Simplifying further:

x <= -1

Therefore, the solution to the inequality 3(x-1) - 4x >= -2 is x <= -1.

Answer 6

try again

Answer 7

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake. Let's try solving the inequality again:

3(x - 1) - 4x >= -2

Distribute the 3 to the terms inside the parentheses:

3x - 3 - 4x >= -2

Combine like terms:

-x - 3 >= -2

Next, add 3 to both sides to isolate the variable term:

-x - 3 + 3 >= -2 + 3

This simplifies to:

-x >= 1

Now, divide both sides by -1. Remember that when dividing by a negative number, the inequality sign flips:

(-x)/(-1) <= 1/(-1)

Simplifying further:

x <= -1

Therefore, the solution to the inequality 3(x-1) - 4x >= -2 is x <= -1.

Answer 8

nope

Answer 9

[AI-generated answer — Bot GPT 3.5]

Apologies for the previous incorrect solutions. Let's solve the inequality correctly this time:

3(x - 1) - 4x > -2

Using the distributive property:

3x - 3 - 4x > -2

Combine like terms:

-x - 3 > -2

Next, add 3 to both sides to isolate the variable term:

-x - 3 + 3 > -2 + 3

This simplifies to:

-x > 1

Now, divide both sides by -1. Remember that when dividing by a negative number, the inequality sign flips:

(-x)/(-1) < 1/(-1)

Simplifying further:

x < -1

Therefore, the solution to the inequality 3(x-1) - 4x > -2 is x < -1.

Answer 10

3(x - 1) - 4x >_ -2

Answer 11

[AI-generated answer — Bot GPT 3.5]

Let's solve the inequality correctly this time:

3(x - 1) - 4x >= -2

Using the distributive property:

3x - 3 - 4x >= -2

Combine like terms:

-x - 3 >= -2

Now, add 3 to both sides to isolate the variable term:

-x - 3 + 3 >= -2 + 3

Simplifying further:

-x >= 1

Finally, divide both sides by -1. Remember that when dividing by a negative number, the inequality sign flips:

(-x)/(-1) <= 1/(-1)

Simplifying further:

x <= -1

Therefore, the solution to the inequality 3(x - 1) - 4x >= -2 is x <= -1.

Answer 12

3(x - 1) - 4x >= -2

Answer 13

[AI-generated answer — Bot GPT 3.5]

Let's solve the inequality step by step:

3(x - 1) - 4x >= -2

Using the distributive property:

3x - 3 - 4x >= -2

Combine like terms:

-1x - 3 >= -2

Now, add 3 to both sides:

-1x - 3 + 3 >= -2 + 3

Simplifying further:

-1x >= 1

Finally, divide both sides by -1. Remember that when dividing/multiplying by a negative number, the inequality sign flips:

(-1x)/(-1) <= 1/(-1)

Simplifying further:

x <= -1

Therefore, the solution to the inequality 3(x - 1) - 4x >= -2 is x <= -1.

Answer 14

3(x - 1) - 4x ≥= -2

Answer 15

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we will first simplify the expression on the left side:

3(x - 1) - 4x >= -2

Distribute the 3 to both terms inside the parentheses:

3x - 3 - 4x >= -2

Combine like terms:

-1x - 3 >= -2

Next, add 3 to both sides to isolate the variable term:

-1x - 3 + 3 >= -2 + 3

Simplifying further:

-1x >= 1

Now, divide both sides by -1. Remember that when dividing/multiplying by a negative number, the inequality sign flips:

(-1x)/(-1) <= 1/(-1)

Simplifying further:

x <= -1

Therefore, the solution to the inequality 3(x - 1) - 4x >= -2 is x <= -1.

Answer 16

NO ITS NOT

Answer 17

[AI-generated answer — Bot GPT 3.5]

Apologies for the confusion. Let's solve the inequality correctly:

3(x - 1) - 4x ≥ -2

Using the distributive property:

3x - 3 - 4x ≥ -2

Combine like terms:

-1x - 3 ≥ -2

To isolate the variable term, we will add 3 to both sides:

-1x - 3 + 3 ≥ -2 + 3

Simplifying further:

-1x ≥ 1

Now, to remove the coefficient in front of x, we need to divide both sides by -1. Remember that when dividing/multiplying by a negative number, the inequality sign flips:

(-1x)/(-1) ≤ 1/(-1)

Simplifying further:

x ≤ -1

Therefore, the solution to the inequality 3(x - 1) - 4x ≥ -2 is x ≤ -1.

Answer 18

5x + 1 < 4x - 2

Answer 19

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we will first simplify the expression on both sides:

5x + 1 < 4x - 2

Next, we will move all the x terms to one side:

5x - 4x < -2 - 1

This simplifies to:

x < -3

Therefore, the solution to the inequality 5x + 1 < 4x - 2 is x < -3.

Answer 20

7x - 7 < 7 (x - 5)

Answer 21

[AI-generated answer — Bot GPT 3.5]

Let's solve the inequality step by step:

7x - 7 < 7(x - 5)

First, distribute the 7 on the right side:

7x - 7 < 7x - 35

Next, let's rearrange the terms to isolate the variable on one side:

7x - 7x < -35 + 7

Simplifying further:

0x < -28

Since any number multiplied by 0 is always 0, the left side of the inequality becomes 0. Thus, we are left with:

0 < -28

However, this statement is not true because 0 is not less than -28.

Therefore, there is no solution to the inequality 7x - 7 < 7(x - 5).

Answer 22

3(1 + x) ≥ 12 - 5x

Answer 23

[AI-generated answer — Bot GPT 3.5]

Let's solve the inequality step by step:

3(1 + x) ≥ 12 - 5x

First, distribute the 3 on the left side:

3 + 3x ≥ 12 - 5x

Next, let's combine like terms (by adding 5x to both sides):

3 + 8x ≥ 12

Now, subtract 3 from both sides:

8x ≥ 12 - 3

Simplifying further:

8x ≥ 9

Finally, divide both sides by 8 to solve for x:

(8x)/8 ≥ 9/8

Simplifying further:

x ≥ 9/8

Therefore, the solution to the inequality 3(1 + x) ≥ 12 - 5x is x ≥ 9/8.

Answer 24

Your cell phone plan costs ​$24.99 per month plus ​$0.18 for each text message you send or receive. You have at most ​$32 to spend on your cell phone bill. What is the maximum number of text messages that you can send or receive next​ month?

Answer 25

[AI-generated answer — Bot GPT 3.5]

To find the maximum number of text messages you can send or receive next month, we need to determine the cost of the text messages and see how many messages you can afford with a budget of $32.

Let's represent the number of text messages as "x".

The cost of the text messages is given by the formula:
Cost = $0.18 per text message * x text messages

So the total cost of the cell phone bill is given by the formula:
Total cost = $24.99 monthly fee + (Cost of text messages)

To find the maximum number of text messages, we will set up the inequality:
Total cost ≤ $32

Using the given information and the formulas above, we can write the inequality as:

$24.99 + ($0.18 * x) ≤ $32

To solve for "x", we can start by subtracting $24.99 from both sides:

$0.18 * x ≤ $32 - $24.99
$0.18 * x ≤ $7.01

Next, divide both sides of the inequality by $0.18 to isolate "x":

x ≤ $7.01 / $0.18
x ≤ 38.94 (rounded to 2 decimal places)

Therefore, the maximum number of text messages you can afford next month is 38 (since you cannot send or receive a fraction of a text message).

Answer 26

Write the following set in roster form and in​ set-builder notation.

N is the set of integers that are greater than -3 and less than or equal to 1

Answer 27

[AI-generated answer — Bot GPT 3.5]

In roster form, the set N can be written as:

N = {-2, -1, 0, 1}

In set-builder notation, the set N can be written as:

N = {x | x is an integer, -3 < x ≤ 1}

Answer 28

Write the set below in roster form and in​ set-builder notation.

P is the set of natural numbers that are less than 11.

Answer 29

[AI-generated answer — Bot GPT 3.5]

In roster form, the set P can be written as:

P = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

In set-builder notation, the set P can be written as:

P = {x | x is a natural number, x < 11}

Answer 30

use ascending order

Answer 31

[AI-generated answer — Bot GPT 3.5]

In roster form, the set P can be written in ascending order as:

P = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

In set-builder notation, the set P can be written as:

P = {x | x is a natural number, x < 11}

Answer 32

Solve the inequality. Write the solution in​ set-builder notation.

-4x - 13 >_ - 29

Answer 33

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we will first isolate the variable term by adding 13 to both sides:

-4x - 13 + 13 ≥ -29 + 13

Simplifying further:

-4x ≥ -16

Next, divide both sides by -4. Remember that when dividing by a negative number, the inequality sign flips:

(-4x)/(-4) ≤ (-16)/(-4)

Simplifying further:

x ≤ 4

Therefore, the solution to the inequality -4x - 13 ≥ -29 can be written in set-builder notation as:

{x | x ≤ 4}

Answer 34

3(2x - 3) < 21

Answer 35

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we will first simplify the expression on the left side:

3(2x - 3) < 21

Using the distributive property:

6x - 9 < 21

Next, add 9 to both sides to isolate the variable term:

6x - 9 + 9 < 21 + 9

Simplifying further:

6x < 30

Finally, divide both sides by 6 to solve for x:

(6x)/6 < 30/6

Simplifying further:

x < 5

Therefore, the solution to the inequality 3(2x - 3) < 21 can be written in set-builder notation as:

{x | x < 5}

Answer 36

Solve the inequality. Write the solution in​ set-builder notation.

-3 (6x + 7) > - 21 - 18x

Answer 37

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we will first simplify the expression on both sides:

-3(6x + 7) > -21 - 18x

Using the distributive property:

-18x - 21 > -21 - 18x

Next, let's rearrange the terms to isolate the variable on one side:

-18x + 18x > -21 + 21

Simplifying further:

0x > 0

Since 0x is always 0, the inequality simplifies to:

0 > 0

However, this statement is not true as 0 is not greater than 0.

Therefore, there is no solution to the inequality -3(6x + 7) > -21 - 18x.

Answer 38

Your test scores in one class are 77 and 83. What possible scores can you earn on your next test to have a test average between 80 and ​86, ​inclusive?

Answer 39

[AI-generated answer — Bot GPT 3.5]

To find the possible scores you can earn on your next test, we need to determine the range of scores that would give you a test average between 80 and 86 inclusive.

Let's denote the score on your next test as "x".

To calculate the average, we add up all the scores (77, 83, and x) and divide by the number of scores (which is 3 in this case).

The average score can be determined using this formula:
Average = (Sum of scores) / (Number of scores)

To find the acceptable range, we'll use the inequality:
80 ≤ Average ≤ 86

Substituting the values, we get:
80 ≤ (77 + 83 + x) / 3 ≤ 86

Multiplying both sides of the inequality by 3 to eliminate the fraction, we get:
240 ≤ 77 + 83 + x ≤ 258

Combining like terms:
240 ≤ 160 + x ≤ 258

Simplifying further:
80 ≤ x ≤ 98

Therefore, the possible scores you can earn on your next test to have a test average between 80 and 86 inclusive are any scores between 80 and 98.

Answer 40

Write a compound inequality that represents the following phrase. Graph the solutions.

all real numbers that are between -3 and 6, inclusive

Answer 41

[AI-generated answer — Bot GPT 3.5]

The compound inequality that represents the given phrase is:

-3 ≤ x ≤ 6

To graph this compound inequality, we will mark -3 and 6 on a number line and shade the interval between them to represent all real numbers that satisfy the inequality.

The graph would look like this:

<---------]¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯[--------->

-3 6

The shaded region between -3 and 6, including -3 and 6, represents the set of all real numbers between -3 and 6 inclusively.

Answer 42

Solve the compound inequality. Graph the solutions.

-11 < 4p - 3 ≤ 29

Answer 43

[AI-generated answer — Bot GPT 3.5]

To solve the compound inequality, we will first solve each inequality separately, and then find the intersection of the two solution sets.

Inequality 1: -11 < 4p - 3

Adding 3 to both sides:
-11 + 3 < 4p - 3 + 3
-8 < 4p

Dividing both sides by 4:
-8/4 < 4p/4
-2 < p

Inequality 2: 4p - 3 ≤ 29

Adding 3 to both sides:
4p - 3 + 3 ≤ 29 + 3
4p ≤ 32

Dividing both sides by 4:
(4p)/4 ≤ 32/4
p ≤ 8

The intersection of the two solution sets is -2 < p ≤ 8.

To graph the solution, we will mark -2 and 8 on a number line with filled circles at -2 and 8, and then shade the interval between them to represent all values of p that satisfy the compound inequality.

The graph would look like this:

-----o===================o------
-2 8

The interval between -2 and 8, including -2 but not including 8, represents the set of values of p that satisfy the compound inequality.

Answer 44

Solve the inequality. Graph the solutions.

5t - 1 < - 36 or 2t + 5 > 9

Answer 45

[AI-generated answer — Bot GPT 3.5]

To solve the inequality, we will examine each inequality separately and graph the solutions.

Inequality 1: 5t - 1 < -36

Adding 1 to both sides:
5t - 1 + 1 < -36 + 1
5t < -35

Dividing both sides by 5:
t < -35/5
t < -7

Inequality 2: 2t + 5 > 9

Subtracting 5 from both sides:
2t + 5 - 5 > 9 - 5
2t > 4

Dividing both sides by 2:

Answer 46

Write the inequality in interval notation. Then graph the interval.

x ≤ - 6 or x > 0