How do you know if a value is a solution for an inequality?
mmmh, I would just sub in the value into the inequality and see it it is true.
To determine if a value is a solution for an inequality, you need to substitute the value into the inequality and check if the resulting statement is true or false. Follow these steps:
1. Begin with the given inequality. For example, let's say we have the inequality 2x + 3 < 10, and we want to check if the value x = 2 is a solution.
2. Substitute the value you want to check into the inequality. In this case, replace x with 2 in the inequality: 2(2) + 3 < 10.
3. Evaluate both sides of the inequality using the substituted value. Simplify the expression on both sides of the inequality: 4 + 3 < 10, which further simplifies to 7 < 10.
4. Determine if the statement is true or false. In this case, 7 is indeed less than 10, so the statement 7 < 10 is true.
5. If the statement is true, then the value you substituted is a solution to the inequality. Therefore, x = 2 is a solution to the inequality 2x + 3 < 10.
Remember, when dealing with inequalities, if the inequality is strict (< or > sign), the solution will not include the value itself (i.e. x < 2, not x ≤ 2). If the inequality is non-strict (≤ or ≥ sign), the solution will include the value as well (i.e. x ≤ 2).