Solving Inequalities Using Addition and Subtraction
Solving Inequalities Using Addition and Subtraction is a Grade 6 math skill from Big Ideas Math Advanced 1, Chapter 7 (Equations and Inequalities) that teaches students to isolate the variable by adding or subtracting the same number from both sides of an inequality, just as with equations. The inequality symbol remains unchanged when adding or subtracting, and the solution represents a range of values rather than a single answer.
Key Concepts
Two inequalities are equivalent if they have the same solution set. The following actions result in an equivalent inequality: Add or subtract the same number on both sides of the inequality.
Common Questions
How do you solve an inequality using addition or subtraction?
Add or subtract the same number from both sides to isolate the variable. The inequality symbol stays the same. For x - 7 > 3: add 7 to both sides to get x > 10. For y + 5 <= 12: subtract 5 from both sides to get y <= 7.
Does the inequality symbol change when adding or subtracting?
No. Adding or subtracting the same number from both sides preserves the inequality relationship. The symbol only changes when multiplying or dividing by a negative number (which is covered separately).
What chapter covers solving inequalities with addition and subtraction in Big Ideas Math Advanced 1?
Solving inequalities using addition and subtraction is covered in Chapter 7 of Big Ideas Math Advanced 1, titled Equations and Inequalities, for Grade 6.
What is an example of solving an inequality by adding?
Solve x - 7 > 3: add 7 to both sides → x > 10. The solution is all numbers greater than 10. On a number line, this is an open circle at 10 with an arrow pointing right.
How is solving an inequality the same as solving an equation?
The process is identical for addition and subtraction: isolate the variable by performing inverse operations on both sides. The key difference is that inequalities have a range of solutions rather than one specific answer.