Solve the Linear Inequality: -2x+ 3 <5
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...
As a rule of thumb, when dealing with inequalities, when we multiply or divide by negative numbers, we have to flip the inequality sign.
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The expression "-2x+3" (red graph) will only be less than "5" (blue graph) in the region when x is greater than -1
-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 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)`
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.