๐ Topic Summary
Solving multi-step inequalities with distribution involves applying the distributive property to remove parentheses, combining like terms, and then isolating the variable. Remember, when you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign! Let's practice these skills to build mastery.
๐ง Part A: Vocabulary
Match the term with its definition:
- Term: Coefficient
- Term: Inequality
- Term: Variable
- Term: Distributive Property
- Term: Solution Set
- Definition: A symbol (usually a letter) representing an unknown value.
- Definition: A statement that compares two expressions using symbols like <, >, โค, or โฅ.
- Definition: The set of all values that satisfy an inequality.
- Definition: The number multiplied by a variable in an algebraic term.
- Definition: $a(b + c) = ab + ac$
โ๏ธ Part B: Fill in the Blanks
When solving inequalities, we use the same steps as solving equations with one exception. If you multiply or ________ both sides of the inequality by a ________ number, you must ________ the inequality sign. The ________ ________ represents all possible answers to the inequality.
๐ค Part C: Critical Thinking
Explain in your own words how solving an inequality is similar to solving an equation and how it is different. Give an example.
๐งฎ Part D: Practice Problems
Solve each inequality:
- ๐งช $2(x + 3) > 10$
- ๐ฌ $-3(y - 2) \leq 15$
- ๐ $4(2z + 1) < 28$
- ๐ $5(a - 4) \geq -5$
- ๐ $-(b + 7) > -12$
- ๐ก $6(c + 2) \leq 30$
- ๐ $-2(d - 1) < 8$