How can you tell if a value is a solution to an inequality.
Substitute the solution variable in the inequation and see if the inequality is satisfied.
For example, if we say x=5 satisfies
x²+2x-10>25
substitute x=5 to get
5²+2*5-10=25
Therefore x=5 is NOT a solution to the given inequation, since the inequality > is violated.
To determine if a value is a solution to an inequality, you need to follow these steps:
Step 1: Understand the inequality and its symbols
Take note of the inequality symbol used in the expression. Common inequality symbols include greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), and not equal to (≠). These symbols are used to compare the value of the variable in question.
Step 2: Substitute the value into the inequality
Replace the variable in the inequality with the given value and evaluate the expression. Make sure to substitute the value in the correct place based on the inequality symbol, i.e., on the left or right side of the inequality.
Step 3: Check if the inequality holds true
If the expression evaluates to true, then the value is a solution to the inequality. In other words, the value satisfies the given condition. If the expression evaluates to false, then the value is not a solution to the inequality.
Here's an example to illustrate the process:
Let's say we have the inequality 2x + 5 > 10 and we want to check if x = 3 is a solution.
Substituting x = 3 into the inequality:
2(3) + 5 > 10
6 + 5 > 10
11 > 10
Since 11 is greater than 10, the inequality holds true. Therefore, x = 3 is a solution to the inequality 2x + 5 > 10.