Question

inequality

-4(7x-3)<12

Answer 1

For this one, here's what to do:

Add -4(7x - 3) to both sides. Then subtract 12 from both sides.

Answer 2

like this

-4(7x - 3+ -4(7x - 3)<12+ -4(7x - 3)

Answer 3

Im so confused

Answer 4

Nope not like that

Answer 5

How will i do it?

Answer 6

If you add 4(7x - 3) to both sides, you get

0 < 12 + 4(7x - 3)

Answer 7

Now try subtracting 12 from both sides.

Answer 8

Not sure how to do that

Like this maybe

0 < 12 + 4(7x - 3)-12?

Answer 9

Subtract 12 from BOTH SIDES. You only subtracted it from one side.

Answer 10

12-0<12+4(7x - 3)-12

Answer 11

Nope you added 12 to the other side rather than subtract it. You have MINUS 12 on one side and PLUS 12 on the other.

Answer 12

Tbh im confused

Answer 13

where do i subtract the 12

Answer 14

Here's what you should have if you subtracted 12 on both sides:
0 -12 < 12 - 12 + 4(7x - 3)

Answer 15

ok

Answer 16

what do i do now?

Answer 17

Simplify the expression. What is 0 - 12 and what is 12 - 12

Answer 18

0

Answer 19

Write the simplified expression after performing those operations.

Answer 20

0 -12 < 12 - 12 + 4(7x - 3)
-12<0+4(7x-3)

Answer 21

which simplifies to -12 < 4(7x - 3)

Answer 22

Now, the next step is to apply the distributive property

Answer 23

ok
-12 < 4(7x - 3)
-12<4*28x-12

like this?

Answer 24

I think you meant to write -12 < 28x - 12

Answer 25

You already multiplied 4 times 7 to get 28 so there's no need to write 4 again.

Answer 26

yes

Answer 27

-12 < 28x - 12
do i solve 28x - 12 now?

Answer 28

You solve for x

Answer 29

The next step is to now add 12 to both sides.

Answer 30

ok
-12+12 < 28x - 12+12

28x>0

Answer 31

28x<0*

Answer 32

I don't know what you did, but I did not mention anything about flipping signs

Answer 33

The inequality is like an arrow. You have to pay attention to where it is pointing.

Answer 34

28x>0 is correct. The other is not.

Answer 35

i didnt mean to flip the sign

Answer 36

Is there more to the problem?

Answer 37

The next step is to divide both sides by 28 to isolate x

Answer 38

ok

Answer 39

28x/28<0/28
x<0
this?

Answer 40

Why do you keep flipping signs?

Answer 41

I only tell you to perform a specific step

Answer 42

idk where the sign goes

Answer 43

I never said ever to flip a sign. That's what confuses students. So I was trying to show you how to do this without flipping the sign

Answer 44

oh

Answer 45

The answer is not x < 0

Answer 46

x<28?

Answer 47

Nope, not that either.

Answer 48

Go back to the last known correct step

Answer 49

oh flip the sign?

Answer 50

idk honestly

Answer 51

Flipping the sign is not a step in the solution I was showing you

Answer 52

You had it mostly right until the very end.

Answer 53

You got it wrong after I told you to divide both sides by 28

Answer 54

oh ok

Answer 55

28x/28<0/28
0<28

Like this idk

Answer 56

I didnt flip signs this time

Answer 57

The last known correct step was 28x > 0. Then if you divide both sides by 28 you get x > 0

Answer 58

Let me show you the full steps though.

Answer 59

Original Problem:
-4(7x-3)<12

Add 4(7x - 3) to both sides to get:
0 < 12 + 4(7x - 3)

Subtract 12 from both sides to get:
-12 < 4(7x - 3)

Apply the distributive property to get:
-12 < 28x - 12

Add 12 to both sides to get
0 < 28x

Divide both sides by 28 to get:
0 < x

This next step is actually not flipping the sign. It is re-arranging the inequality so that x is on the LHS:
x > 0

At no point did I flip a sign. Flipping the sign is an entirely different process.

Answer 60

Ok this is much clearer

Answer 61

In fact, you could leave it as 0 < x