Solving Multi-Step Inequalities with Word Problems

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 combining like terms, distributing, and isolating the variable.

Front

How do you solve the inequality -2x + 3(-4x + 6) ≤ 116?

Back

First, distribute: -2x - 12x + 18 ≤ 116. Combine like terms: -14x + 18 ≤ 116. Subtract 18: -14x ≤ 98. Divide by -14 (flip the sign): x ≥ -7.

Front

What does it mean to flip the inequality sign?

Back

Flipping the inequality sign occurs when you multiply or divide both sides of an inequality by a negative number.

Front

What is the solution to the inequality 4(2a + 3) < 3(a - 1)?

Back

Distribute: 8a + 12 < 3a - 3. Subtract 3a: 5a + 12 < -3. Subtract 12: 5a < -15. Divide by 5: a < -3.

Front

How do you represent a word problem as an inequality?

Back

Identify the quantities involved, determine the relationship (greater than, less than, etc.), and express it using variables and constants.

Front

What is the inequality for a taxi ride costing $1.75 plus $0.75 per mile if you have $20?

Back

0.75n + 1.75 ≤ 20, where n is the number of additional miles.

Front

What does the inequality 22 < 6c + 4 represent?

Back

It represents a relationship where 6 times a variable c, plus 4, must be greater than 22.

Front

What is the solution to the inequality 3x ≥ 12?

Back

Divide both sides by 3: x ≥ 4.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than or less than another.

Front

What does the term 'solution set' mean in the context of inequalities?

Back

The solution set is the set of all values that satisfy the inequality.