An example of an inequality equation is 5x - 4 > 2x + 3.
Understanding Inequality Equations
Inequality equations, unlike equality equations (=), use symbols like > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to) to show a relationship between expressions. They don't state that two expressions are equal, but rather that one is greater than, less than, or greater/less than or equal to the other.
- Example: The inequality 5x - 4 > 2x + 3 means that the expression "5x - 4" is greater than the expression "2x + 3". Solving this inequality involves finding the range of x values that make this statement true.
The provided reference states: "The expression 5x − 4 2x + 3 looks like an equation but with the equals sign replaced by an arrowhead. It is an example of an inequality. This denotes that the part on the left, 5x − 4, is greater than the part on the right, 2x + 3." This perfectly illustrates the concept. While the reference uses an arrowhead, the standard mathematical symbol for "greater than" is ">".
Let's clarify the reference's example: The inequality 5x - 4 > 2x + 3 can be solved by:
- Subtracting 2x from both sides: 3x - 4 > 3
- Adding 4 to both sides: 3x > 7
- Dividing both sides by 3: x > 7/3 or x > 2.333...
This means any value of x greater than 7/3 will satisfy the inequality.
Here are a few more examples of inequality equations:
- x + 2 ≤ 8
- 2y - 5 > 10
- 3z + 1 < 0
- -4w ≥ 12
