Systems of Inequalities Word Problems

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

How do you represent a constraint in a word problem as an inequality?

Back

Identify the key quantities and their relationships, then express the constraints using inequality symbols (>, <, ≥, ≤) based on the context.

Front

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

Back

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

Front

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

Back

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

Front

What is the difference between a system of equations and a system of inequalities?

Back

A system of equations has specific solutions (one, none, or infinitely many), while a system of inequalities can have a range of solutions represented by a shaded region.

Front

How do you graph a system of inequalities?

Back

Graph each inequality on the same coordinate plane, using dashed lines for '<' or '>' and solid lines for '≤' or '≥'. The solution is the overlapping shaded region.

Front

What is the significance of the shaded region in a graph of inequalities?

Back

The shaded region represents all possible solutions that satisfy the inequality. Points in this region are valid solutions.

Front

How do you write an inequality for a maximum constraint?

Back

Use the '≤' symbol to indicate that the quantity cannot exceed a certain value.

Front

How do you write an inequality for a minimum constraint?

Back

Use the '≥' symbol to indicate that the quantity must be at least a certain value.

Front

If a problem states 'at most 40 coins', how would you express this as an inequality?

Back

You would express this as 'd + q ≤ 40', where d is the number of dimes and q is the number of quarters.