Solving One-Step Inequalities Using Multiplication or Division
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 11: Inequalities) learn to solve one-step inequalities using multiplication or division. The critical rule is that multiplying or dividing both sides by a negative number reverses the inequality sign direction.
Key Concepts
To solve an inequality using multiplication or division, multiply or divide both sides by the same positive or negative number. If you multiply or divide by a negative number, you must reverse the inequality sign. If you multiply or divide by a positive number, the inequality sign stays the same.
Common Questions
How do you solve one-step inequalities with multiplication or division in 7th grade?
Multiply or divide both sides by the same number. If positive, the inequality sign stays the same. If negative, reverse the inequality sign. Example: solving -2y <= 8 gives y >= -4 (divide by -2, flip sign).
Why do you flip the inequality sign when dividing by a negative number?
Dividing by a negative reverses the order of numbers on the number line. For example, 4 > 2, but -4 < -2. So the inequality direction must flip to remain true.
How do you solve 3x > 15?
Divide both sides by 3 (positive number, sign stays same): x > 5.
What chapter in Big Ideas Math Advanced 2 covers solving inequalities with multiplication?
Chapter 11: Inequalities in Big Ideas Math Advanced 2 (Grade 7) covers solving one-step inequalities using multiplication or division.
How do you solve an inequality with a fraction like x/4 < 7?
Multiply both sides by 4 (positive, sign stays): x < 28.