Verifying Solutions to Inequalities
Verifying Solutions to Inequalities is a Grade 6 math skill from Big Ideas Math Advanced 1, Chapter 7 (Equations and Inequalities) that teaches students to check whether specific values satisfy an inequality by substituting them and evaluating the truth of the resulting statement. Students test the boundary value plus values on both sides to confirm the complete solution set before graphing.
Key Concepts
To verify if a value is a solution to an inequality, substitute the value for the variable and check if the resulting statement is true. Test the boundary value and values on both sides to confirm the complete solution set.
Common Questions
How do you verify a solution to an inequality?
Substitute the value into the inequality and check if the resulting statement is true. Always test the boundary value first, then test values on both sides to determine the full solution set. For x >= 3: test x=3 (boundary), x=4 (solution), and x=2 (not a solution).
Why test the boundary value when verifying inequality solutions?
The boundary value determines whether the inequality uses strict inequality (< or >) or includes equality (<= or >=). Testing it reveals whether the boundary point is included in the solution set.
What chapter covers verifying inequality solutions in Big Ideas Math Advanced 1?
Verifying solutions to inequalities is covered in Chapter 7 of Big Ideas Math Advanced 1, titled Equations and Inequalities, a Grade 6 math textbook.
What is an example of verifying a solution to an inequality?
For 2x + 1 < 7: test x=2 → 2(2)+1=5 < 7 (true, solution). Test x=3 → 2(3)+1=7 < 7 (false, not a solution). Test x=4 → 2(4)+1=9 < 7 (false, not a solution). So x=2 is a solution but x=3 is not.
How does verification help before graphing an inequality?
Verification confirms which values satisfy the inequality, ensuring you graph in the correct direction and use the right type of endpoint (open circle for strict inequalities, filled circle for <= or >=).