Solving Two-Step Linear Inequalities
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 11: Inequalities) learn to solve two-step linear inequalities of the form ax + b < c by applying inverse operations in order. The key rule is to reverse the inequality sign only when multiplying or dividing both sides by a negative number.
Key Concepts
A two step linear inequality has the form $ax + b < c$, $ax + b \leq c$, $ax + b c$, or $ax + b \geq c$, where $a \neq 0$. To solve a two step inequality, use the same steps as solving a two step equation, but reverse the inequality sign when multiplying or dividing both sides by a negative number.
Common Questions
How do you solve a two-step linear inequality in 7th grade?
Step 1: Add or subtract to isolate the variable term. Step 2: Multiply or divide to solve for the variable. If you divide or multiply by a negative number, reverse the inequality sign.
How do you solve 3x + 7 > 16?
Subtract 7 from both sides: 3x > 9. Divide by 3: x > 3.
How do you solve -2y + 5 <= 11?
Subtract 5 from both sides: -2y <= 6. Divide by -2 and reverse sign: y >= -3.
What chapter in Big Ideas Math Advanced 2 covers solving two-step linear inequalities?
Chapter 11: Inequalities in Big Ideas Math Advanced 2 (Grade 7) covers solving two-step linear inequalities.
How is solving a two-step inequality different from a two-step equation?
The process is the same except that multiplying or dividing by a negative number reverses the inequality symbol, which does not happen with equations.