Question

A solution to the compound inequality 16 > 4 - 3x > -11 is provided below. Choose the statement that is true about the given solution.




16 > 4 - 3x and 4 - 3x > -11

Line 1


12 > -3x and -3x > -15

Line 2


-4 > x and x > 5

Line 3


There is a mistake in line # 1.

There is a mistake in line # 2.

There is a mistake in line # 3.

There are no mistakes, the solution is correct.

Answer 1

16 > 4 - 3x
16 - 4 > -3x
12 > - 3x (when dividing by a negative, the sign changes)
-4 < x

4 - 3x > -11
-3x > -11 - 4
-3x > -15
x < 5

line 2 is wrong

Answer 2

thank you so much

Answer 3

no problem :)

Answer 4

can I ask you one more question!?

Answer 5

yes you can :)

Answer 6

Select the inequality that corresponds to the given graph.

a number line graph with a closed circle at negative 6, shading to the left.

3x - 7 < 11

-4x greater than or equal to 24

-2x + 7 less than or greater to 13

3(x - 2) - 3 greater than or equal to x - 5

Answer 7

For the first problem:
Lines 1 and 2 are correct.
Line 3 is wrong.

Answer 8

oh...I was looking at the problem wrong...I was thinking line two was below not above

Answer 9

mathstudent is correct then...it is line 3

Answer 10

Quick lesson : if it is greater then, shading goes to the right, if it is less then, shading goes to the left. If there is an equal sign involved, it is a closed circle,if no equal sign is involved, it is an open circle

Answer 11

so what do you think the answer is ?

Answer 12

ok so would it be the third one?

Answer 13

For the secpnd problem, since the graph has a closed circle, the answer has to have \(\ge\) or \(\le\), but not plain > or <.
This eliminates choice A.
Now you need to solve the inequalities of choices B, C, and D. to see which one has the solution \(x \le -6\).

Answer 14

oh so its B

Answer 15

right?

Answer 16

sorry let me check

Answer 17

ok I think it is B

Answer 18

-4x >= 24
x <= -6.....correct...it is B

Answer 19

thank you! ok this is thhlast one I promise -2y - 7 > 11

Part 1: Solve the inequality above.
Part 2: Describe the graph of the solution.

Answer 20

can you solve the inequality ?

Answer 21

remember when dividing by a negative, the inequality sign changes

Answer 22

is it y < -2?

Answer 23

-2x - 7 > 11
now add 7 to both sides
-2x > 18
now divide by -2....changing the sign
x > -9
Do you understand what I just did ?

Answer 24

oops...I put x's....supposed to be y's

Answer 25

yes you made that very understandable. ok so its y > -9?

Answer 26

the sign changes....I am sorry...answer is y < -9

Answer 27

ok so what would the graph look like?

Answer 28

if it is less then shading to the left, if it is greater then, shading to the right.
equal signs mean closed circles, no equal signs means open circles. What do you think the graph is ?