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

- moongazer

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

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- schrodinger

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- moongazer

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

- hoblos

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

- anonymous

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- JamesJ

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.

- moongazer

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

- moongazer

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

- JamesJ

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)

- moongazer

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

- moongazer

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

- moongazer

???

- JamesJ

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

- moongazer

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

- JamesJ

Yes

- moongazer

because x is negative right ?

- moongazer

thanks

- JamesJ

No. It is true that
-6x>-3 ==> x< 3/6
because you just multiplied both sides by a negative number, -1/6

- JamesJ

x itself could be negative or positive or zero.

- JamesJ

So, have you been able to replicate this solution now:
-6x+10 > 7 Or -6x +10 <-7
x<1/2 x>17/6

- JamesJ

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

- moongazer

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

- moongazer

yes or no ???

- JamesJ

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.

- JamesJ

I'll leave you to it now.

- moongazer

Thanks!

- moongazer

:)

- moongazer

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?

- JamesJ

yes

- moongazer

Thank You
I just wanted to know.
:)

- JamesJ

***Correction to post above:
In case 2, when -6x+10 < 0, we have
| -6x + 10 | > 7 ==> -(-6x+10) > 7
==> 6x-10 > 7 [NOT -7]

- moongazer

ok :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.