Linear Inequalities and Systems of Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

Front

What does the solution set of a linear inequality represent?

Back

The solution set of a linear inequality represents all the possible values that satisfy the inequality.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the appropriate region based on the inequality symbol.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

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

Back

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

Front

What is the maximum number of hours a DJ can play if the total cost must be under $600, given the DJ charges $125 per hour and $55 for an assistant?

Back

The inequality representing this situation is 125x + 55 < 600.

Front

If four times a number increased by 7 is at least 19, what is the inequality?

Back

The inequality is 4x + 7 ≥ 19.

Front

How do you find the greatest number of rides Daniel can go on if he can spend no more than $40, with admission costing $10 and rides costing $1.50 each?

Back

The inequality representing this situation is 1.50x + 10 ≤ 40.

Front

What does the inequality y < 2x + 3 represent in terms of graphing?

Back

It represents a region below the dashed line of the equation y = 2x + 3.