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}
{x|x is less than or equal to 2 thirds}
Question 1:
The inequalities with x = 3 as a solution are:
a) x + 3 < 4(x + 1) + 2
b) 2x - 8 ≥ 7 - 3x
c) 3(x + 2) < 14 - x
d) 4(x - 1) < x + 5
e) 5 - 2( x + 1) > x
f) 6(x - 4) ≤ 2x
Question 2:
The line that shows the inequality after combining like terms is Line B: 4x + 4 + 8 ≥ 4 + 2x
Question 3:
The possible next steps for Mari to solve the inequality 4(x - 3) > 16 are:
a) 4x - 12 + 12 > 16 + 12
b) 4x - 12 - (-12) > 16 - (-12)
e) 4(4x - 12) > 16(4)
Question 4:
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:
The solution set of the inequality 3( - 1 - x) ≤ -2x - 3x is: {x|x≥3/2}
1.) To identify the inequality with x = 3 as a solution, you can substitute 3 for x in each inequality and see if it holds true.
a) x + 3 < 4(x + 1) + 2
Substitute x = 3:
3 + 3 < 4(3 + 1) + 2
6 < 4(4) + 2
6 < 16 + 2
6 < 18
This means that x = 3 is not a solution to this inequality.
b) 2x - 8 ≥ 7 - 3x
Substitute x = 3:
2(3) - 8 ≥ 7 - 3(3)
6 - 8 ≥ 7 - 9
-2 ≥ -2
This means that x = 3 is a solution to this inequality.
c) 3(x + 2) < 14 - x
Substitute x = 3:
3(3 + 2) < 14 - 3
3(5) < 11
15 < 11
This means that x = 3 is not a solution to this inequality.
d) 4(x - 1) < x + 5
Substitute x = 3:
4(3 - 1) < 3 + 5
4(2) < 8
8 < 8
This means that x = 3 is not a solution to this inequality.
e) 5 - 2( x + 1) > x
Substitute x = 3:
5 - 2(3 + 1) > 3
5 - 2(4) > 3
5 - 8 > 3
-3 > 3
This means that x = 3 is not a solution to this inequality.
f) 6(x - 4) ≤ 2x
Substitute x = 3:
6(3 - 4) ≤ 2(3)
6(-1) ≤ 6
-6 ≤ 6
This means that x = 3 is a solution to this inequality.
Therefore, the inequalities with x = 3 as a solution are:
- 2x - 8 ≥ 7 - 3x
6(x - 4) ≤ 2x
2.) The inequality "4(x + 1) + 8 ≥ 4 + 2x" can be simplified by combining like terms.
Line A: 4(x + 1) + 8 ≥ 4 + 2x
Simplify:
4x + 4 + 8 ≥ 4 + 2x
Combine like terms:
4x + 12 ≥ 4 + 2x
The line that shows the inequality after combining like terms is Line C: 4x + 12 ≥ 4 + 2x.
3.) To determine the next step in solving the inequality "4(x - 3) > 16" after the step "4x - 12 > 16", we can consider the operations used in the previous step.
The step "4x - 12 > 16" subtracted 12 from both sides of the inequality. So, the next step should undo this operation by adding 12 to both sides.
Option A) "4x - 12 + 12 > 16 + 12" adds 12 to both sides, which is the correct next step.
Therefore, the next step could be A) 4x - 12 + 12 > 16 + 12.
4.) Javon and Ivy are given the inequality "5 - 2x - 13 ≤ 4" and they have different first steps.
Javon's first step is "-2x - 13 ≤ 9".
To determine if Javon is incorrect, we need to determine if his step is incorrect. To do this, we need to simplify the inequality and check if it holds true.
Start with the given inequality: "5 - 2x - 13 ≤ 4".
Simplify by combining like terms: "-2x - 8 ≤ 4".
Since Javon's step of "-2x - 13 ≤ 9" is not equivalent to the given inequality, Javon is incorrect.
Therefore, the answer is D) Javon is incorrect because, on his first step, he did not subtract 5 (or equivalently add -5) from both sides of the equation.
5.) To find the solution set of the inequality "3(-1 - x) ≤ -2x - 3x", we need to simplify the inequality and solve for x.
Start with the given inequality: "3(-1 - x) ≤ -2x - 3x".
Simplify inside the parentheses: "3(-1) - 3x ≤ -2x - 3x".
Simplify further: "-3 - 3x ≤ -5x".
To solve for x, we will isolate the variable on one side of the inequality.
Add 5x to both sides: "-3 - 3x + 5x ≤ -5x + 5x".
Simplify: "2x - 3 ≤ 0".
Add 3 to both sides: "2x - 3 + 3 ≤ 0 + 3".
Simplify: "2x ≤ 3".
Divide by 2 to solve for x: "x ≤ 3/2".
So, the solution set of the inequality is x ≤ 3/2.
Therefore, the answer is B) {x|x≤32} or {x|xis less than or equal to 3 halves}.