what are the answers
1.) ldentify the inequality with x = 3 as a solution. Select all that apply.(3 points)
a) x + 3 < 4(x + 1) + 2
x + 3 < 4(x + 1) + 2
B) 2x - 8 ≥ 7 - 3x
2x - 8 ≥ 7 - 3x
c) 3(x + 2) < 14 - x
3(x + 2) < 14 - x
d) 4(x - 1) < x + 5
4(x - 1) < x + 5
e) 5 - 2( x + 1) > x
5 - 2( x + 1) > x
f) 6(x - 4) ≤ 2x
6(x - 4) ≤ 2x
Question 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
and Which Line shows the inequality after you combine like terms?
Responses
Line B
Line B
Line C
Line C
Line D
Line D
Line E
Line E
Line F
Line F
Question 3
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.
(3 points)
Responses
A) 4x - 12 + 12 > 16 + 12
4x - 12 + 12 > 16 + 12
B) 4x - 12 - (-12) > 16 - (-12)
4x - 12 - (-12) > 16 - (-12)
C) (14)(4x − 12) > 16 (1(4))(14)(4x − 12) > 16 (1(4))
D) 4x4 − 12 > 1644x4 − 12 > 164
E) 4(4x - 12) > 16(4)
4(4x - 12) > 16(4)
Question 4
Javon and Ivy are both given the equation 5 − 2x−13 ≤ 4. Javon thinks the first step is − 2x−13 ≤ 9. Ivy thinks the first step is −2x− 13 ≤ −1. Who is incorrect and why?(1 point)
Responses
A) Ivy is incorrect because, on her first step, she did not add 5 (or equivalently subtract -5) from both sides of the equation.
Ivy is incorrect because, on her first step, she did not add 5 (or equivalently subtract -5) from both sides of the equation.
B) 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 multiply by 3 on both sides of the equation.
C) Both students are incorrect because, on their first step, they did not divide by 3 (or equivalently multiply by 13) from 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 third) from both sides of the equation.
D) Javon is incorrect because, on his first step, he did not subtract 5 ( or equivalently add -5) 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.
Question 5
Consider the inequality 3( - 1 - x) ≤ -2x - 3x.
The solution set of the inequality is:
(1 point)
Responses
A) {x|x≥32}
{x|xis greater than or equal to 3 halves}
B) {x|x≤32}
{x|xis less than or equal to 3 halves}
C) {x|x≥23}
{x|xis greater than or equal to 2 thirds}
D){x|x≤23}
The answers are as follows:
1.) The inequalities that have x = 3 as a solution are:
a) x + 3 < 4(x + 1) + 2
c) 3(x + 2) < 14 - x
d) 4(x - 1) < x + 5
2.) The line that shows the inequality after combining like terms is Line C: 4x + 12 ≥ 4 + 2x
3.) The next step for Mari's inequality 4(x - 3) > 16 could be:
a) 4x - 12 + 12 > 16 + 12
b) 4x - 12 - (-12) > 16 - (-12)
e) 4(4x - 12) > 16(4)
4.) Ivy is incorrect because, on her first step, she did not add 5 (or equivalently subtract -5) from both sides of the equation.
5.) The solution set of the inequality 3(-1 - x) ≤ -2x - 3x is: {x | x ≥ 3/2} (Option A)
To find the answers to the questions, follow these steps:
1.) For question 1, we need to identify the inequality with x = 3 as a solution. To do this, we substitute x = 3 into each inequality and check if it is true. From the provided options, you can see that a), b), c), and d) have x + 3 in their inequality. Therefore, the correct answers are options a) x + 3 < 4(x + 1) + 2, b) 2x - 8 ≥ 7 - 3x, c) 3(x + 2) < 14 - x, and d) 4(x - 1) < x + 5.
2.) For question 2, we need to determine which line shows the inequality after combining like terms. Looking at the given lines, you can see that line B) 4x + 4 + 8 ≥ 4 + 2x is the one where like terms have been combined. Therefore, the answer is line B.
3.) For question 3, we are asked to identify the next step in solving the inequality 4(x - 3) > 16. To find the next step, we need to simplify the inequality. From the given options, you can see that option E) 4(4x - 12) > 16(4) represents the next step of distributing the 4 to both terms inside the parentheses. Therefore, the answer is option E.
4.) For question 4, we are asked to determine who is incorrect between Javon and Ivy in solving the equation 5 − 2x−13 ≤ 4. To determine this, we need to examine their first steps. Ivy's first step is −2x− 13 ≤ −1, while Javon's first step is − 2x−13 ≤ 9. From these steps, we can see that Javon is incorrect because he did not subtract 5 (or equivalently add -5) from both sides of the equation. Therefore, the answer is Javon is incorrect because, on his first step, he did not subtract 5 (or equivalently add -5) from both sides of the equation.
5.) For question 5, we are given the inequality 3( - 1 - x) ≤ -2x - 3x and asked to find the solution set. To do this, we need to simplify the inequality and solve for x. By simplifying the inequality, we get -3 - 3x ≤ -5x. Now we can solve for x by isolating the variable. Subtracting -5x from both sides gives us 2x ≥ 3, which simplifies to x ≥ 3/2 or x is greater than or equal to 3/2. Therefore, the answer is A) {x|x≥32} or {x|xis greater than or equal to 3 halves}.
The answers to the questions are as follows:
1) The inequalities with x = 3 as a solution are:
- x + 3 < 4(x + 1) + 2
- 4(x - 1) < x + 5
- 6(x - 4) ≤ 2x
2) The Line that shows the inequality after combining like terms is:
- Line B: 4x + 4 + 8 ≥ 4 + 2x
3) The possible next step for Mari's inequality 4(x - 3) > 16 is:
- Step A: 4x - 12 + 12 > 16 + 12
- Step B: 4x - 12 - (-12) > 16 - (-12)
- Step E: 4(4x - 12) > 16(4)
4) Javon is incorrect because on his first step, he did not subtract 5 (or equivalently add -5) from both sides of the equation.
5) The solution set of the inequality 3(-1 - x) ≤ -2x - 3x is:
- {x|x≥32}