Writing, Solving, and Graphing Two-Step Inequalities

Front

What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable, typically involving addition or subtraction followed by multiplication or division.

Front

How do you represent a word problem as an inequality?

Back

Identify the variable, determine the relationship described in the problem, and translate the words into mathematical symbols, using inequality signs appropriately.

Front

What does the symbol '<' represent in an inequality?

Back

The symbol '<' means 'less than' and indicates that the value on the left side is smaller than the value on the right side.

Front

What does the symbol '>' represent in an inequality?

Back

The symbol '>' means 'greater than' and indicates that the value on the left side is larger than the value on the right side.

Front

How do you solve the inequality 2x + 5 < 3x?

Back

Subtract 2x from both sides to get 5 < x, which simplifies to x > 5.

Front

What is the first step in solving the inequality -10x + 5 ≥ 195?

Back

Subtract 5 from both sides to isolate the term with the variable: -10x ≥ 190.

Front

What is the solution to the inequality -10x + 5 ≥ 195?

Back

x ≤ -19.

Front

How do you graph the solution of an inequality on a number line?

Back

Use an open circle for '<' or '>' and a closed circle for '≤' or '≥'. Shade the region that represents the solution set.

Front

What is the significance of the daily operating cost in a profit equation?

Back

The daily operating cost represents the fixed costs that must be covered before any profit can be made.

Front

How do you set up an equation to find when two fans pay the same amount for tickets?

Back

Set the total costs of both fans equal to each other and solve for the variable representing the number of games.