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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.
4x + 16 = 0
4x = -16
x = -4 the root of the equation and it is a single value.
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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