Solve the Linear Inequality:

-2x+ 3 <5

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-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) **

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

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.

-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.

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