difference between solving equation and inequalitydifference between solving equation and inequality

Expert Answers
hala718 eNotes educator| Certified Educator

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 | Student

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.