Is Number Solution to Inequality
Working with inequalities gives a range of solutions for an equation. For example, if you have the inequality x > 2, the answer can be any number that is greater than 2. So, the following numbers are all solutions to the inequality x > 2: 2.01, 8, 100, 591465. 2 is not a solution, and nor is any number less than 2 (1.9, 0, -98).
To work out if a number is a solution to an inequality, you'll need to first solve the equation. You can do this either by reducing the equation so that x (or another algebraic term) is on its own, or by plugging in a value for x.
Solving the equation
If you are given the equation:
You can solve the equation until you are just left with x on one side.
First, combine the like terms on the right-hand side
Then subtract 5 from both sides to leave x on its own:
Therefore, x is less than 4. That means that any number less than 4 is a solution for x (3.9, 0, -986).
Plugging in a solution
The other method you can use is to plug in a proposed number for x and see if the equation works.
If you have the equation:
You can pick a number for x and see if the equation works. So, for example, we could choose 10. Plugging that in gives us:
Working that through, we get:
7 is less than 14, so 10 is a correct solution.
If we chose 100 as the number to plug in we'd get:
97 is not less than 14, so 100 is not a correct solution.
This is the simplest way to find out if a single number is a solution, but to find out a range of numbers that work, you should solve the problem to its simplest form first.