How do you know if a value is a solution for an inequality? How is this different from determining if a value is a solution to an equation? If you replace the equal sign of an equation with an inequality sign, is there ever a time when the same value will be a solution to both the equation and the inequality? Write an inequality and provide a value that may or may not be a solution to the inequality.
To determine if a value is a solution for an inequality, you need to substitute the value into the inequality and check whether it satisfies the inequality's conditions. Unlike equations, inequalities involve greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠) symbols.
The main difference between determining solutions for inequalities and equations is that equations require the value to satisfy the exact equality, whereas inequalities only require the value to satisfy the inequality's conditions.
If you replace the equal sign of an equation with an inequality sign, there are cases where the same value can be a solution for both the equation and the inequality. For example, if you have the equation "x = 5" and the inequality "x ≤ 5," the value x = 5 satisfies both the equation and the inequality since it is equal to 5 and also less than or equal to 5.
Now, let's write an inequality and provide a value that may or may not be a solution to the inequality. Consider the inequality "2x + 3 > 7." To determine if the value x = 2 is a solution, substitute it into the inequality:
2(2) + 3 > 7
4 + 3 > 7
7 > 7
Since 7 is not greater than 7 but rather equal to 7, the inequality is not satisfied. Hence, x = 2 is not a solution to the inequality "2x + 3 > 7."