A1 - Inequalities in Two Variables, Word Problems

Front

What is an inequality in two variables?

Back

An inequality in two variables is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, or ≥) and involves two variables, typically represented as x and y.

Front

How do you represent a word problem as an inequality?

Back

To represent a word problem as an inequality, identify the quantities involved, determine the relationship between them, and express that relationship using inequality symbols.

Front

What does the symbol ≤ mean in an inequality?

Back

The symbol ≤ means 'less than or equal to'. It indicates that the value on the left side of the inequality is either less than or equal to the value on the right side.

Front

What does the symbol ≥ mean in an inequality?

Back

The symbol ≥ means 'greater than or equal to'. It indicates that the value on the left side of the inequality is either greater than or equal to the value on the right side.

Front

How do you solve an inequality?

Back

To solve an inequality, isolate the variable on one side of the inequality sign using inverse operations, similar to solving an equation. Remember to reverse the inequality sign when multiplying or dividing by a negative number.

Front

What is the difference between < and ≤?

Back

The symbol < means 'less than', while ≤ means 'less than or equal to'. The former does not include the value itself, whereas the latter does.

Front

What is the difference between > and ≥?

Back

The symbol > means 'greater than', while ≥ means 'greater than or equal to'. The former does not include the value itself, whereas the latter does.

Front

How can you graph an inequality in two variables?

Back

To graph an inequality in two variables, first graph the corresponding equation as a line. Then, use a dashed line for < or > (not including the line) and a solid line for ≤ or ≥ (including the line). Shade the appropriate region based on the inequality.

Front

What is a feasible region in the context of inequalities?

Back

A feasible region is the area on a graph that satisfies all the inequalities in a system. It represents all possible solutions to the inequalities.

Front

What is the significance of the boundary line in an inequality?

Back

The boundary line in an inequality separates the graph into two regions: one that satisfies the inequality and one that does not. The line itself may or may not be included in the solution set, depending on whether the inequality is strict or inclusive.