Checking Solutions by Substitution
Checking solutions by substitution in inequalities is a Grade 7 algebra skill in Big Ideas Math Advanced 2, Chapter 11: Inequalities. To verify a solution, substitute the given value for the variable and evaluate both sides — if the resulting inequality is true, the value is a solution; if false, it is not. For example, x equals 3 is a solution to 2x plus 1 is less than or equal to 9 because substituting gives 7 which is less than or equal to 9.
Key Concepts
To check if a value is a solution to an inequality, substitute the value for the variable and evaluate both sides. If the resulting statement is true, the value is a solution. If false, it is not a solution.
Common Questions
How do you check if a value is a solution to an inequality?
Substitute the value for the variable in the inequality, evaluate both sides, and check if the resulting statement is true. If true, the value is a solution; if false, it is not.
How is checking solutions for inequalities different from equations?
The process is the same, but instead of checking if both sides are equal, you check whether the inequality sign is satisfied. A true inequality statement confirms the value is in the solution set.
Is a value equal to the boundary solution of an inequality?
For inequalities with equals (less than or equal to, greater than or equal to), boundary values are solutions. For strict inequalities (less than, greater than), boundary values are not solutions.
What textbook covers checking solutions to inequalities in Grade 7?
Big Ideas Math Advanced 2, Chapter 11: Inequalities covers checking solutions by substitution for inequalities.