FA 8-2: Two-Step Inequalities Word Problems

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable. For example, in the inequality 2x + 3 < 7, you would first subtract 3 from both sides and then divide by 2.

Front

Define the variable in the context of word problems.

Back

Defining the variable means assigning a symbol (usually a letter) to represent an unknown quantity in a problem, making it easier to set up an equation or inequality.

Front

What does the inequality 15 + 6x ≤ 100 represent in a real-world context?

Back

It represents a situation where a fixed cost of $15 plus a variable cost of $6 per person must not exceed a total budget of $100.

Front

How do you solve a two-step inequality?

Back

To solve a two-step inequality, perform the inverse operations in reverse order: first, isolate the term with the variable, and then isolate the variable itself.

Front

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

Back

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

Front

Write the inequality that represents Joan's situation of needing $100 for a calculator, given her earnings.

Back

5x + 10 ≥ 100, where x is the number of hours she babysits.

Front

What is the first step in solving the inequality 7n - 1 > 76?

Back

The first step is to add 1 to both sides of the inequality, resulting in 7n > 77.

Front

What does it mean to graph an inequality?

Back

Graphing an inequality means representing the solutions of the inequality on a number line, showing which values satisfy the inequality.

Front

What is the solution to the inequality 5x + 10 ≥ 100?

Back

x ≥ 18, after isolating x by subtracting 10 and dividing by 5.

Front

What is the significance of the maximum or minimum in word problems involving inequalities?

Back

The maximum or minimum indicates the limits within which the variable must fall to satisfy the conditions of the problem.