Give Solutions to Inequality
When you solve an inequality, you get a range of solutions. If you get the equation , the answer can be any number less than 8. So, dealing only with integers, the solutions are and so on.
To give the solutions to an inequality we need to use Interval Notation, which is a way of showing a range using only the ends of the interval.
To give a range of solutions to an inequality, we first have to solve the equation.
If we're given:
We would first combine the like terms to get:
Therefore the solutions to the problem are any number greater than -6 (but not -6 itself) and any number smaller than 16 (which could include 16). In other words, the integer solutions are:
To write this out with interval notations we would set the intervals as -6 and 16. Because the solution has to be greater than, but can't equal, -6 we use the curved bracket; because it can equal 16 we use a square bracket. That gives us:
If we take another equation:
We would subtract 2 from both sides to isolate the x:
So, the solutions to the equation are any numbers greater than 3 (but not 3 itself).
Since just above 3 is our lowest interval, we use a curved bracket and the number (3. The highest possible solution is infinite, so we use the infinity symbol and a square bracket ∞].
Therefore, the range of solutions is (3,∞].