Identify the inequality with x = 3 as a solution. Select all that apply.

Question

x + 3 < 4(x + 1) + 2

2x - 8 ≥ 7 - 3x

3(x + 2) < 14 - x

4(x - 1) < x + 5

5 - 2( x + 1) > x

6(x - 4) ≤ 2x

Answer 1

To find the inequality with x = 3 as a solution, substitute 3 for x in each inequality and see if the resulting statement is true.

x + 3 < 4(x + 1) + 2
3 + 3 < 4(3 + 1) + 2
6 < 4(4) + 2
6 < 16 + 2
6 < 18
This inequality is true when x = 3.

2x - 8 ≥ 7 - 3x
2(3) - 8 ≥ 7 - 3(3)
6 - 8 ≥ 7 - 9
-2 ≥ -2
This inequality is true when x = 3.

3(x + 2) < 14 - x
3(3 + 2) < 14 - 3
15 < 14 - 3
15 < 11
This inequality is false when x = 3.

4(x - 1) < x + 5
4(3 - 1) < 3 + 5
8 < 8
This inequality is false when x = 3.

5 - 2( x + 1) > x
5 - 2(3 + 1) > 3
5 - 2(4) > 3
5 - 8 > 3
-3 > 3
This inequality is false when x = 3.

6(x - 4) ≤ 2x
6(3 - 4) ≤ 2(3)
6(-1) ≤ 6
-6 ≤ 6
This inequality is true when x = 3.

Therefore, the inequalities with x = 3 as a solution are:
x + 3 < 4(x + 1) + 2
2x - 8 ≥ 7 - 3x
6(x - 4) ≤ 2x

Answer 2

The following inequality is solved for x.

Line A 4(x + 1) + 8 ≥ 4 + 2x

Line B 4x + 4 + 8 ≥ 4 + 2x

Line C 4x + 12 ≥ 4 + 2x

Line D 2x + 12 ≥ 4

Line E 2x ≥ - 8

Line F x ≥ -4

Which Line shows the inequality after you combine like terms?

Line B

Line C

Line D

Line E

Line F

Answer 3

The Line that shows the inequality after combining like terms is Line C: 4x + 12 ≥ 4 + 2x.

Answer 4

Mari is solving the inequality 4(x - 3) > 16. Her first step is 4x - 12 > 16.

Which step could be the next step? Select all that apply.

4x - 12 + 12 > 16 + 12

4x - 12 - (-12) > 16 - (-12)

(14)(4x − 12) > 16 (1(4))

4x4 − 12 > 164

4(4x - 12) > 16(4)

Answer 5

The next step could be:

4x - 12 + 12 > 16 + 12
This step involves adding 12 to both sides of the inequality.

Answer 6

Mari is solving the inequality 4(x - 3) > 16. Her first step is 4x - 12 > 16.
Which step could be the next step? Select all that apply.

4x - 12 + 12 > 16 + 12

4x - 12 - (-12) > 16 - (-12)

(1/4)(4x-12)>16(1/(4))

4x/4-12>16/4

4(4x - 12) > 16(4)

Answer 7

The next steps could be:

4x - 12 + 12 > 16 + 12
This step involves adding 12 to both sides of the inequality.

4x - 12 - (-12) > 16 - (-12)
This step involves subtracting -12 (which is the same as adding 12) to both sides of the inequality.

4(4x - 12) > 16(4)
This step involves multiplying both sides of the inequality by 4.

Answer 8

Javon and Ivy are both given the equation 5-2x-1/3≤4 Javon thinks the first step is -2x-1/3≤9 Ivy thinks the first step is -2x-1/3≤-1 Who is incorrect and why?

Ivy is incorrect because, on her first step, she did not add 5 (or equivalently subtract -5) from both sides of the equation.

Both students are incorrect because, on their first step, they did not multiply by 3 on both sides of the equation.

Both students are incorrect because, on their first step, they did not divide by 3 (or equivalently multiply by 1/3) from both sides of the equation.

Javon is incorrect because, on his first step, he did not subtract 5 ( or equivalently add -5) from both sides of the equation.

Answer 9

Both students are incorrect because, on their first step, they did not add 5 (or equivalently subtract -5) from both sides of the equation.

Answer 10

Javon and Ivy are both given the equation 5-2x-1/3≤4 Javon thinks the first step is -2x-1/3≤9 Ivy thinks the first step is -2x-1/3≤-1 Who is incorrect and why?

Ivy is incorrect because, on her first step, she did not add 5 (or equivalently subtract -5) from both sides of the equation.

Both students are incorrect because, on their first step, they did not multiply by 3 on both sides of the equation.

Both students are incorrect because, on their first step, they did not divide by 3 (or equivalently multiply by 1/3) from both sides of the equation.

Javon is incorrect because, on his first step, he did not subtract 5 ( or equivalently add -5) from both sides of the equation.

Consider the inequality 3( - 1 - x) ≤ -2x - 3x

Answer 11

I cannot determine who is incorrect based on the given information. The inequality given (3(-1 - x) ≤ -2x - 3x) is different from the equation mentioned in the previous question (5-2x-1/3≤4).

Answer 12

Javon and Ivy are both given the equation 5-2x-1/3≤4 Javon thinks the first step is -2x-1/3≤9 Ivy thinks the first step is -2x-1/3≤-1 Who is incorrect and why?

Ivy is incorrect because, on her first step, she did not add 5 (or equivalently subtract -5) from both sides of the equation.

Both students are incorrect because, on their first step, they did not multiply by 3 on both sides of the equation.

Both students are incorrect because, on their first step, they did not divide by 3 (or equivalently multiply by 1/3) from both sides of the equation.

Javon is incorrect because, on his first step, he did not subtract 5 ( or equivalently add -5) from both sides of the equation.

Answer 13

Javon is incorrect because, on his first step, he did not subtract 5 (or equivalently add -5) from both sides of the equation.

Answer 14

Javon and Ivy are both given the equation 5-2x-1/3≤4 Javon thinks the first step is -2x-1/3≤9 Ivy thinks the first step is -2x-1/3≤-1 Who is incorrect and why?

1. Ivy is incorrect because, on her first step, she did not add 5 (or equivalently subtract -5) from both sides of the equation.

2. Both students are incorrect because, on their first step, they did not multiply by 3 on both sides of the equation.

3. Both students are incorrect because, on their first step, they did not divide by 3 (or equivalently multiply by 1/3) from both sides of the equation.

4. Javon is incorrect because, on his first step, he did not subtract 5 ( or equivalently add -5) from both sides of the equation.

Answer 15

Option 4 is correct. Javon is incorrect because, on his first step, he did not subtract 5 (or equivalently add -5) from both sides of the equation.

Answer 16

Consider the inequality 3( - 1 - x) ≤ -2x - 3x.

The solution set of the inequality is:

1. {x|x≥3/2}

2. {x|x≤3/2}

3. {x|x≥2/3}

4. {x|x≤2/3}

Answer 17

To solve the inequality, let's simplify it step by step:

3(-1 - x) ≤ -2x - 3x

To simplify the left side of the inequality:

3(-1 - x) = -3 - 3x

Now, we have:

-3 - 3x ≤ -2x - 3x

Simplifying the right side of the inequality:

-2x - 3x = -5x

Now, we have:

-3 - 3x ≤ -5x

To isolate the variable x, let's add 5x to both sides:

-3 - 3x + 5x ≤ -5x + 5x

This simplifies to:

2x - 3 ≤ 0

To isolate the variable x, let's add 3 to both sides:

2x - 3 + 3 ≤ 0 + 3

This simplifies to:

2x ≤ 3

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

(2x)/2 ≤ (3)/2

This simplifies to:

x ≤ 3/2

Therefore, the solution set of the inequality is:

{x | x ≤ 3/2}

So, option 2, {x | x ≤ 3/2}, is the correct solution set for the inequality.

Answer 18

Solve the inequality: -2(2x - 4) ≤ 4(2 - x)

x ≤ 0

x ≤ 4

x ≤ 8

All Real Numbers

No Solution

Answer 19

To solve the inequality, let's simplify it step by step:

Starting with the given inequality:

-2(2x - 4) ≤ 4(2 - x)

Let's distribute the -2 on the left side and the 4 on the right side:

-4x + 8 ≤ 8 - 4x

Now, let's simplify the inequality:

-4x + 8 ≤ 8 - 4x

It can be observed that the terms -4x and -4x cancel out, leaving:

8 ≤ 8

This inequality is true for all values of x. Therefore, the solution to the inequality is:

All Real Numbers

Thus, the correct answer is: All Real Numbers.

Answer 20

Which values are in the solution set of the inequality -2/3x+13≥-1 ?

19

20

21

22

23

Answer 21

To find the solution set of the inequality, we'll solve it step by step:

-2/3x + 13 ≥ -1

First, let's subtract 13 from both sides:

-2/3x ≥ -1 - 13

-2/3x ≥ -14

Now, let's multiply both sides by -3/2 (flipping the inequality due to multiplication by a negative number):

(-3/2)(-2/3x) ≤ (-3/2)(-14)

This simplifies to:

x ≤ 21

Therefore, the values in the solution set of the inequality are x ≤ 21.

Among the options provided, the values in the solution set are:

19
20
21

So, the correct answer is 21.

Answer 22

Which values are in the solution set of the inequality -2/3x+13≥-1 ?

select all that apply

19

20

21

22

23

Answer 23

To find the solution set of the inequality, we'll solve it step by step:

-2/3x + 13 ≥ -1

Let's subtract 13 from both sides:

-2/3x ≥ -1 - 13

-2/3x ≥ -14

Now, let's multiply both sides by -3/2 (flipping the inequality due to multiplication by a negative number):

(-3/2)(-2/3x) ≤ (-3/2)(-14)

This simplifies to:

x ≤ 21

Therefore, the values in the solution set of the inequality are x ≤ 21.

Among the options provided:

19 is ≤ 21, so it is in the solution set.
20 is ≤ 21, so it is in the solution set.
21 is ≤ 21, so it is in the solution set.
22 is not ≤ 21, so it is not in the solution set.
23 is not ≤ 21, so it is not in the solution set.

Thus, the values that are in the solution set are: 19, 20, and 21.

Answer 24

x blank 5blank x blank 18

The above compound inequality is true only if blank of the statement(s) is/are true.

none

all

at least 1

Answer 25

The above compound inequality is true only if at least 1 of the statement(s) is true.

Answer 26

x blank 5 blank x blank 18

inequality

Answer 27

To find the inequality represented by the expression "x blank 5 blank x blank 18," we need to determine the relationships between x, 5, and 18.

The possible relationships are:

1) x < 5 and x < 18 (x is less than both 5 and 18)
2) x ≤ 5 and x < 18 (x is less than or equal to 5, but still less than 18)
3) x < 5 and x ≤ 18 (x is less than 5, but still less than or equal to 18)
4) x ≤ 5 and x ≤ 18 (x is less than or equal to both 5 and 18)

Without more specific information about the inequality, we cannot determine the exact relationship between x, 5, and 18. Therefore, we cannot provide a specific inequality.

Answer 28

Solve for x.
18 > 2x + 4 ≥ 4

14 < x ≤ 4

7 > x > 8

7 > x ≥ 12

7 > x ≥ 4

7 > x ≥ 0

Answer 29

To solve for x in the inequality 18 > 2x + 4 ≥ 4, we'll break it down into two separate inequalities:

First, 2x + 4 ≥ 4:

Subtract 4 from both sides:

2x ≥ 0

Divide both sides by 2:

x ≥ 0

Now, the second inequality, 18 > 2x + 4:

Subtract 4 from both sides:

14 > 2x

Divide both sides by 2:

7 > x

Combining both inequalities, we have:

7 > x ≥ 0

Therefore, the solution for x is given by the inequality 7 > x ≥ 0.

Answer 30

For which compound inequalities is 6 a solution? Select the statements that are true.

-5 < x < 6

-2 ≤ x ≤ 6

x ≤ 2 or x ≥ 6

x < 2 or x > 6

x < -5 or x > 0

Answer 31

To determine if 6 is a solution to each compound inequality, substitute x = 6 into each inequality and check if the statement is true.

-5 < x < 6
-5 < 6 < 6
This inequality is false when x = 6.

-2 ≤ x ≤ 6
-2 ≤ 6 ≤ 6
This inequality is true when x = 6.

x ≤ 2 or x ≥ 6
6 ≤ 2 or 6 ≥ 6
This inequality is true when x = 6.

x < 2 or x > 6
6 < 2 or 6 > 6
This inequality is false when x = 6.

x < -5 or x > 0
6 < -5 or 6 > 0
This inequality is false when x = 6.

Based on the evaluations, the statements that are true and have 6 as a solution are:

-2 ≤ x ≤ 6

x ≤ 2 or x ≥ 6

Answer 32

For which compound inequalities is 6 a solution? Select the statements that are true.
select all 3 that apply
-5 < x < 6

-2 ≤ x ≤ 6

x ≤ 2 or x ≥ 6

x < 2 or x > 6

x < -5 or x > 0

Answer 33

To determine if 6 is a solution to each compound inequality, substitute x = 6 into each inequality and check if the statement is true.

-5 < x < 6
-5 < 6 < 6
This inequality is false when x = 6.

-2 ≤ x ≤ 6
-2 ≤ 6 ≤ 6
This inequality is true when x = 6.

x ≤ 2 or x ≥ 6
6 ≤ 2 or 6 ≥ 6
This inequality is true when x = 6.

x < 2 or x > 6
6 < 2 or 6 > 6
This inequality is false when x = 6.

x < -5 or x > 0
6 < -5 or 6 > 0
This inequality is false when x = 6.

Based on the evaluations, the statements that are true and have 6 as a solution are:

-2 ≤ x ≤ 6

Answer 34

For which compound inequalities is 6 a solution is x < -5 or x > 0

Answer 35

A student scored 85 in her Algebra class before she took the End of Course Exam (the EOC). The student wants her average to be between 80 and 90 inclusive after her EOC is entered into her grades. The EOC counts 1/5 of her overall grade and her class average counts 4/5 of her grade. Write and solve a compound inequality to find the possible score she will need to make on the EOC to get the average she wants for her final grade in the course.

1. 80≤85+85+85+85+x/5≤90;85≤x≤110

2. 80<85+85+85+85+x/5<90;85<x<110

3. 90≤85+85+85+85+x/5≤80;110≤x≤80

4. 90<85+85+85+85+x/5<80;110<x<80

Answer 36

x≤5andx<18

The above compound inequality is true only if blank of the statement(s) is/are true

none

all

at least 1