8 Questions
What is the solution set for the inequality 2x + 3y < 6?
The set of all points (x, y) that satisfy the inequality
For the inequality -3x + 4y >= 12, what region does the solution set lie in?
The region above the line
What happens to the solution set of an inequality 4x - 5y > 20 if both sides of the inequality are divided by a negative number?
The solution set flips across the x-axis
Which type of line represents the boundary for an inequality 3x - 2y <= 6?
A solid line
In the inequality 5x - 3y > 15, what happens to the solution set if both sides of the inequality are multiplied by a negative number?
The inequality sign changes, and the solution set is reversed.
For the inequality -2x + 7y < 21, in which region does the solution set lie?
Above the line represented by -2x + 7y = 21.
Which type of line represents the boundary for the inequality 6x - y > 12?
Solid line with a shading above it.
What is the solution set for the inequality 4x + 5y ≤ 20?
$4x + 5y < 20$
Study Notes
Inequality Solution Sets
- The solution set for the inequality 2x + 3y < 6 lies in the region where the value of the expression is less than 6.
- The solution set for the inequality -3x + 4y >= 12 lies in the region where the value of the expression is greater than or equal to 12.
Boundary Lines
- The boundary for the inequality 3x - 2y <= 6 is a solid line, indicating that the points on the line are included in the solution set.
- The boundary for the inequality 6x - y > 12 is a dashed line, indicating that the points on the line are not included in the solution set.
Effect of Operations on Solution Sets
- If both sides of an inequality are divided by a negative number, the direction of the inequality is reversed, and the solution set is also reversed.
- If both sides of an inequality are multiplied by a negative number, the direction of the inequality is reversed, and the solution set is also reversed.
- The solution set for the inequality 4x - 5y > 20 is reversed if both sides of the inequality are divided by a negative number.
- The solution set for the inequality 5x - 3y > 15 is reversed if both sides of the inequality are multiplied by a negative number.
Specific Inequalities
- The solution set for the inequality 4x + 5y ≤ 20 lies in the region where the value of the expression is less than or equal to 20.
- The solution set for the inequality -2x + 7y < 21 lies in the region where the value of the expression is less than 21.
Test your knowledge on linear inequalities in two variables with this quiz. Explore the solution sets, regions, and the impact of dividing both sides by a negative number in different inequality scenarios.
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