2 Variable inequality

Front

What is a two-variable inequality?

Back

A two-variable inequality is a mathematical statement that compares two expressions involving two variables, typically written in the form of 'ax + by <, >, ≤, or ≥ c'.

Front

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

Back

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

Front

How do you graph a two-variable inequality?

Back

To graph a two-variable inequality, first graph the corresponding equation as a line. Then, use a dashed line for '<' or '>' and a solid line for '≤' or '≥'. Finally, shade the appropriate region based on the inequality.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all ordered pairs (x, y) that satisfy the inequality.

Front

Is (0, 0) a solution to the inequality y ≥ 2x - 2?

Back

No, because substituting (0, 0) gives 0 ≥ -2, which is true, but (0, 0) is not included in the solution set.

Front

Which inequality matches the graph showing a solid line and shaded above?

Back

The inequality is y ≥ mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If a point lies on the boundary line of an inequality, it means that the point satisfies the equation of the line, and whether it is included in the solution set depends on the type of inequality (solid or dashed line).

Front

How do you determine if a point is a solution to an inequality?

Back

To determine if a point is a solution to an inequality, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the inequality representing Allen's watering situation?

Back

The inequality is 0.7s + 0.5r ≤ 11, where s is the number of sunflower plants and r is the number of rose bushes.