difference between solving equation and inequalitydifference between solving equation and inequality

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hala718's profile pic

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

Posted on

I will explain in an example:

We have the equation:

2x + 5 = 9

We will solve the equation by isolating x on the left side.

We will subtract 5 from both sides.

==> 2x = 4

==> x = 2

Then there is only one solution to the equation which is x =2.

Now we will solve the equality:

2x + 5 < 9

We will follow the same procedure for solving the equation by isolating x on the left side.

==> 2x < 4

==> x < 2

Now unlike the equation, the answer is an interval.

Then solution is any real number belongs to the interval ( -inf , 2 )

==> x = ( -inf , 2)

 

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The difference between the results of an equation and an inequality, would be better said.

The result of an equation is called root of that equation and it is a distinct number.

The result of an inequality is a range of values. If the value of the variable is located in the established range, the inequality is holding.

Equation:

4x + 16 = 0

4x = -16

x = -4 the root of the equation and it is a single value.

Inequality:

4x-16 < 0

4x < 16

x < 4

For any value of x, located in the range (-infinite, 4), the inequality is holding.

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