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Concept explainers
Solve for the unknown variable from the inequality equation.
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Answer to Problem 25PT
Explanation of Solution
Given:
The inequality equation:
Concept Used:
In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. a ≠ b says that a is not equal to b. a < b says that a is less than b. a > b says that a is greater than b.
There are four different types of inequalities:
Greater than −
For Inequality equation: If
Rules for solving inequality equations:
These things do not affect the direction of the inequality:
- Add (or subtract) a number from both sides
- Multiply (or divide) both sides by a positive number
- Simplify a side
But these things do change the direction of the inequality ("
- Multiply (or divide) both sides by a negative number
- Swapping left and right hand sides
Calculation:
The inequality equation:
Solve:
Solution set:
An open circle is used for greater than (>) or less than (<). The point is not part of the solution. The graph then extends endlessly in one direction
Solution set on the number line
Solution of the inequality equation is
Thus, the solution of the inequality equation
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