Question

|-6x+10|>7
show your solutions please.

Answer 1

|-6x+10|>7
I already get on how to solve this

Answer 2

-6x+10 > 7 Or -6x +10 <-7
x<1/2 x>17/6

Answer 3

Well moongazer whenever an expression is inside a mod function then you have to consider two cases either positive or negative that is what hobolos replied

Answer 4

Whenever you have an equation | stuff | > c, then you need to consider two cases.

1. If stuff > 0, then by definition of absolute value | stuff | = stuff and therefore
| stuff | > c => stuff > c

This is now an ordinary algebra inequality that you can solve. That is the first case you have here:
-6x + 10 > 7

2. There if of course a second case: stuff < 0. In which case, by definition of absolute value | stuff | = - stuff and therefore
| stuff | > c => -stuff > c.

That is the second case you have here
-(-6x+10) > 7


Now take these two cases and solve them. That's the algebraic approach.

Answer 5

so I can multiply first the -6x+10 by - before applying the rules?

Answer 6

I am just confused when to change < to this > or vice versa.

Answer 7

By definition if y < 0, then
|y| = -y.

For example, if y = -3, then |y| = |-3| = 3 = -y.



Write here y = -6x + 10.

If y = -6x + 10 < 0, then
|y| = |-6x + 10|
= -(-6x+10)

Answer 8

if x is negative isn't it I need to change < to >

Answer 9

This is my only question
if x is negative isn't it I need to change < to >

Answer 10

???

Answer 11

Whenever you have an inequality

a < b

if you multiply both sides by a negative number then the inequality changes. For instance
a < b ==> -2a > -2b
a < b ==> -17a > -17b
a < b ==> -a > -b

Answer 12

like -6x>-3 to x< 3/6

Answer 13

Yes

Answer 14

because x is negative right ?

Answer 15

thanks

Answer 16

No. It is true that
-6x>-3 ==> x< 3/6

because you just multiplied both sides by a negative number, -1/6

Answer 17

x itself could be negative or positive or zero.

Answer 18

So, have you been able to replicate this solution now:

-6x+10 > 7 Or -6x +10 <-7
x<1/2 x>17/6

Answer 19

If so, I want to show you one other way to tackle the problem.

Answer 20

Will the answer be the same if I did 6x-10 > 7 Or 6x -10 <-7 ??
cause I think it will

Answer 21

yes or no ???

Answer 22

In case 1, when -6x + 10 > 0, we have

| -6x + 10 | > 7 ==> (-6x+10) > 7
==> 6x-10 < -7



In case 2, when -6x+10 < 0, we have

| -6x + 10 | > 7 ==> -(-6x+10) > 7
==> 6x-10 > -7


So the answer to your question is yes. But it's very important to understand why. If you just blindly try to use rules for problem solving without understanding how they relate the definition and properties of the mathematics objects you're using, you're certain to get into trouble sooner or later.

Answer 23

I'll leave you to it now.

Answer 24

Thanks!

Answer 25

:)

Answer 26

I have another question
in an ordinary equality or inequality
if I multiplied the left side by negative; do I also need to multiply the right side by negative?

Answer 27

yes

Answer 28

Thank You
I just wanted to know.
:)

Answer 29

***Correction to post above:

In case 2, when -6x+10 < 0, we have

| -6x + 10 | > 7 ==> -(-6x+10) > 7
==> 6x-10 > 7 [NOT -7]

Answer 30

ok :)