Question

Solve for x: −2x + 5 < 7


x > −1

x < −1

x > −6

x < −6

Answer 1

solve it like you would an equation :)
−2x + 5 < 7 add 2x to both sides
+2x +2x
5 < 7 + 2x subtract 7 from both sides
-7 -7
-2 < 2x then divide both sides by 2
/2 /2

Answer 2

First, let's work on the left hand side of your inequality, the -2x + 5
This means, for instance, to see if it can be simplified at all.
Multiply x and 2
Multiply x and 1


The x just gets copied along.

The answer is x

x

2*x evaluates to 2x

Because of the minus sign

2x becomes - 2x

The answer is -2x

-2*x+5 evaluates to -2x+5

So, all-in-all, the left hand side of your inequality can be written as: -2x+5

Now, let's work on the right hand side of your inequality, the 7
The right hand side of your inequality can be written as: 7
So with these (any) simplifications, the inequality we'll set out to solve is:
-2x+5 ‹ 7

Move the 5 to the right hand side by subtracting 5 from both sides, like this:
From the left hand side:
5 - 5 = 0

The answer is -2x

From the right hand side:
7 - 5 = 2

The answer is 2


Now, the inequality reads:
-2x ‹ 2
To isolate the x, we have to divide both sides of the inequality by the other "stuff" (variables or coefficients)
around the x on the left side of the inequality.

The last step is to divide both sides of the inequality by -2 like this:
To divide x by 1


The x just gets copied along in the numerator.

The answer is x

-2x ÷ -2 = x


2 ÷ -2 = -1


Note! Here's an important point about inequalities:
We are now dividing by -2, which is a number less than zero! This changes the form of your inequality. Or, in other words, your ‹ will now become a ›.

The solution to your inequality is:
x › -1
So, your solution is:
x must be greater than -1

Answer 3

-1

Answer 4

There's no need to move them around that much.


−2x + 5 < 7
-5 -5

-2x < 2
/-2 /-2

x > -1

When you divide or multiply by a negative you flip the sign.

Answer 5

wow thanks guys. :)

Answer 6

@mangorox why do you keep copying and pasting?

Answer 7

in that case, you type really really fast 0.o

Answer 8

lol you do

Answer 9

Yeah...I type fast...also because I've done this question for homework before so...

Answer 10

oh nice

Answer 11

1) Why did you delete the post you tagged me?

2) How do you type 250 words in like 2 seconds? o.o

Answer 12

@tHe_FiZiCx99
1) I didn't delete the post, must be something with OpenStudy.

2) I was typing shortly after @jigglypuff314 was typing...so for about 1-2 minutes.

Answer 13

Lol what?! The question opened and jiggly puff was already typing ._.

Answer 14

@tHe_FiZiCx99 I said I started typing after jiggly puff posted his comment...so I typed for more than "2 seconds". Probably about 1-2 minutes...

Answer 15

o.o ok...