Algebra Keystone Module 1 Practice Test (2025)

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

What does the inequality x + y ≤ 30 represent in a real-world context?

Back

It represents a constraint where the total number of mysteries (x) and biographies (y) in a display cannot exceed 30.

Front

How do you interpret the inequality 2x ≤ 3y?

Back

This inequality indicates that for every 2 mysteries, there can be at least 3 biographies, establishing a ratio between the two.

Front

What is the significance of the solution (6 mysteries and 22 biographies) in the context of the inequalities?

Back

This solution satisfies both inequalities, meaning it is a valid combination of mysteries and biographies that can be displayed.

Front

What is a graph of a system of inequalities?

Back

A graph of a system of inequalities shows the region where all inequalities overlap, representing all possible solutions.

Front

What does the equation y = 15x + 30 represent?

Back

This equation represents a linear relationship where y (total money paid) increases by $15 for each month (x) the customer rents the storage unit.

Front

How do you find a solution to the equation y = 15x + 30?

Back

To find a solution, substitute a value for x (months) and calculate y (total money paid). For example, if x = 16, then y = 15(16) + 30 = 270.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is less than, greater than, less than or equal to, or greater than or equal to the other.

Front

How do you solve the inequality 5x – 6 < 4 + 6x?

Back

To solve, first isolate x by rearranging the inequality: 5x - 6 < 4 + 6x becomes -6 < 4 + x, then x > -10.

Front

What does the equation b = 25w + 100 represent?

Back

This equation represents the total number of baseball cards (b) in Keyshawn's collection after w weeks, starting with 100 cards and adding 25 each week.