How to solve for x values:      -3x + 2 < 5

Expert Answers
hala718 eNotes educator| Certified Educator

-3x + 2 < 5

We will solve it the same way we solve any equation:

First subtract 2 from both sides:

==> -3x < 3

Now divide by (-3)

==> x > -1  

(Notice that we changed the direction of the inequality because we divided by a negative number. Every time you multiply or divide by a negative number, you change the direction of the inequality).

Now x values belong to the interval (-1, inf.)

To check:

Substitute with 0:

-3(0) + 2 < 5

2< 5

giorgiana1976 | Student

The first step is to isolate the term in x to the left side of the inequality.

For this reason , we'll add -2 both sides of the inequality, for the inequality to hold:

-3x+2-2<5-2

-3x<3

We'll divide by -3, both sides of the inequality.

Do not forget to change the direction of the inequality because you've divided the inequality by a negative value:

x>3/-3

x>-1

That means that the inequality holds for any value of x from the interval (-1, +infinity).

Pay attention that the interval is open to the left side, meaning that for the value of x = -1, the inequality doesn't hold.

neela | Student

-3x+2 < 5. To solve for x

Solution:

-3x+2 < 5. 

To solve the inequality we add equals to both sides, which does ot affect the inequality.So we add -2 to both sides.

-3x+2+(-2) < 5+(-2).

-3x  <  3.

We can devide both sides by positive equals without affecting the inequality> So we divide by 3.

-3x/3 <  3/3

-x < 1.

We can multiply both sides of an inequality by -1, but we should reverse the inequality.

-x*(-1) < 1*(-1). In equality sign reverses by multiplication of -1.

x < -1