Question

Solve -4x - 5 > -9 and describe the graph of the solution.

x > 1; closed circle on 1, shading to the right

x < 1; closed circle on 1, shading to the left

x < 1; open circle on 1, shading to the left

x > 1; open circle on 1, shading to the right

Answer 1

What did you do to solve this problem?

Answer 2

No i need help solving it

Answer 3

Right. And the word "help" often implies that you do part of it. Thus my question. What did you do already, so we don't have to cover that material again?

Answer 4

No Im saying i dont understand how to solve it.

Answer 5

Okay, that's not good. Can you solve this for m? 4m = 12

Answer 6

m=8

Answer 7

No, sorry. It requires division. If 4m = 12, then (4m)/4 = 12/4 and m = 3

Let's try another one. 3w + 2 = 11

Answer 8

oh yeah sorry, i forget.

Answer 9

w=3

Answer 10

Excellent: 3w + 2 = 11
Subtract 2: 3w = 9
Divide by 3: w = 3

One more: 3w + 2 > 11

Answer 11

3w>9

Answer 12

oh wait hold on

Answer 13

w>3

Answer 14

Perfect. Now let's tackle your original problem.

-4x - 5 > -9

Add 5

-4x > -4

What's next?

Answer 15

x>-1

Answer 16

No, not quite. Two things wrong with it.

1) (-4)/(-4) = +1
2) Division by a Negative Number requires you to do WHAT with the inequality?

Answer 17

Do i need to flip the sign?

Answer 18

-4x > -4 leads by division to x < 1

Answer 19

so i needed to flip it?

Answer 20

I don't know what "flip" means. Let me try to suggest another way that compeltely avoids any confusion.

-4x > -4

Add 4

-4x + 4 > 0

Add 4x

4 > 4x

Divide by 4

1 > x

This way, we never divided by a negative number and no one will have to remember to do anything with the inequality. It just is what it is.

Answer 21

im still not getting it. but thank you for trying

Answer 22

1 > x is the same as x < 1 -- right?

Answer 23

yes

Answer 24

Super. Now, take a good, hard look at the third answer WAY UP at the top.