# difference between solving equation and inequalitydifference between solving equation and inequality

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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)**

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.**