ALG X: 3.5 Multi-Step Inequalities w/Variables on BOTH sides

Front

Solve the inequality: 4 - 2x ≥ 10 - 3x

Back

x ≥ 6

Front

Solve the inequality: 2x + 3 < 5x - 2

Back

x > 5/3

Front

Solve the inequality: 2(x - 1) + 3 > 4(x + 2) - 1

Back

x < -3

Front

A car rental company charges a flat fee of $50 plus $25 per day for renting a car. You have at most $200 to spend. How many days can you rent the car for?

Back

6

Front

Solve the inequality: 3(x - 2) > 2(x + 1)

Back

x > 8

Front

Definition: Multi-Step Inequality

Back

An inequality that requires more than one step to solve, often involving combining like terms and isolating the variable.

Front

Key Principle: Isolating the Variable

Back

To solve an inequality, you must isolate the variable on one side of the inequality sign.

Front

Definition: Inequality Sign

Back

A symbol that shows the relationship between two expressions, indicating that one is greater than, less than, or equal to the other.

Front

Example: Solving Inequalities with Variables on Both Sides

Back

To solve 2x + 3 < 5x - 2, subtract 2x from both sides to get 3 < 3x - 2.

Front

Key Concept: Reversing the Inequality Sign

Back

When multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be reversed.