Homework Help

Solve the Linear Inequality: -2x+ 3 <5

user profile pic

calraedwards | Student, College Freshman | (Level 2) eNoter

Posted November 26, 2010 at 2:01 AM via web

dislike 0 like

Solve the Linear Inequality:

-2x+ 3 <5

4 Answers | Add Yours

Top Answer

user profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted November 26, 2010 at 2:02 AM (Answer #1)

dislike 2 like

-2x+ 3 <5

First we will subtract 3 from both sides:

==> -2x + 3 - 3 < 5 - 3

==> -2x < 2

Now we will divide by -2:

(remember that when dividing or multiplying by a negative number, you must change the direction of the inequality)

==> -2x/ -2  >   2/ -2

==> x > -2

Then the solution is :

x belongs to the interval ( -2, infinity)

user profile pic

changchengliang | Elementary School Teacher | (Level 2) Adjunct Educator

Posted November 26, 2010 at 2:05 AM (Answer #2)

dislike 0 like

The task is to find the range for x such that:
-2x+ 3 < 5
As of solving all algebraic equations and inequalities, the motivation is to make the unknown the subject.  We do so by systematically getting rid of terms which are in the way.

First, we want to get rid of the 3 on the LHS (left hand side) by minusing 3 on both sides:
-2x+ 3 -3 < 5 -3
-2x    <  2

Next, we want to get rid of the coefficient in front of the x.  To be exact, actually we are trying to reduce it to 1.  We do so by dividing both sides by "-2".  But...

WARNING
As a rule of thumb, when dealing with inequalities, when we multiply or divide by negative numbers, we have to flip the inequality sign.

Therefore,  x>-1

To be convinced of the solution,

Click on the link provided at the bottom of this answer.

The expression "-2x+3" (red graph) will only be less than "5" (blue graph) in the region when x is greater than -1

user profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted November 26, 2010 at 2:15 AM (Answer #3)

dislike 0 like

To solve the linear inequality :-2x+3 < 5.

Thegiven inequality :

-2x+3 < 5.

We add -2x to both sides:

-2x+3 +2x < 5 +2x.

Then we get:

3 < 5+2x.

We subtract 5 from both sides:

3-5 < 5+2x-5.

 Then we get:

-2 <  2x.

We divide  both sides by 2:

-2/2 < 2x/2.

Then we get:

-1 < x.

Therefore the solution of the given inequality is is : x > -1.

 

user profile pic

tonys538 | Student, Undergraduate | TA | (Level 1) Valedictorian

Posted January 1, 2015 at 9:44 AM (Answer #4)

dislike 0 like

The inequality -2x+ 3 <5 has to be solved.

In solving an inequality keep the following points in mind:

Any term can be added to or subtracted from both the sides without changing the inequality. There is also no change if both the sides are multiplied by a positive number.

The sign of the equality reverses if both the sides are multiplied by a negative number.

For the given inequality -2x+ 3 <5

Subtract 3 from both the sides, we get:

-2x + 3 - 3 < 5 - 3

-2x < 2

Multiply both the sides by -1/2. As both sides are multiplied by a negative number the sign of the inequality is reversed.

(-1/2)*(-2x) > 2*(-1/2)

x > -1

The solution of the inequality is the set of values `(-1, oo)`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes