Multi-Step Inequalities (Distributive Property)

Front

What is a multi-step inequality?

Back

A multi-step inequality is an inequality that requires more than one step to solve, often involving operations like addition, subtraction, multiplication, or division.

Front

What does the distributive property state?

Back

The distributive property states that a(b + c) = ab + ac, meaning you can distribute a number across a sum inside parentheses.

Front

How do you solve the inequality -2(x + 2) < 14?

Back

First, distribute -2: -2x - 4 < 14. Then, add 4 to both sides: -2x < 18. Finally, divide by -2 and flip the inequality: x > -9.

Front

What happens to the inequality symbol when you multiply or divide by a negative number?

Back

You must flip the inequality symbol when you multiply or divide both sides of an inequality by a negative number.

Front

Solve the inequality 3x - 5 > -26.

Back

Add 5 to both sides: 3x > -21. Then, divide by 3: x > -7.

Front

What is the solution to the inequality 6(n + 2) < -72?

Back

First, distribute 6: 6n + 12 < -72. Then, subtract 12: 6n < -84. Finally, divide by 6: n < -14.

Front

Solve the inequality 3(m + 7) < 28.

Back

Distribute 3: 3m + 21 < 28. Subtract 21: 3m < 7. Finally, divide by 3: m < 7/3.

Front

What is the first step in solving a multi-step inequality?

Back

The first step is to simplify the inequality, which may involve distributing or combining like terms.

Front

What does it mean to isolate the variable in an inequality?

Back

Isolating the variable means to get the variable on one side of the inequality by performing inverse operations.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that make the inequality true.