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 symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left can be greater than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed line (for < or >) or a solid line (for ≤ or ≥). Then shade the appropriate region based on the inequality.

Tags

CCSS.HSA.REI.D.12

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality, represented graphically by the shaded region on the graph.

Tags

CCSS.HSA.REI.D.12

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' represents a dashed line and does not include the line itself, while 'y ≤ mx + b' includes the line, represented by a solid line.

Tags

CCSS.HSA.REI.D.12

Front

If a band wants to spend no more than $75 on fliers, what type of inequality would represent this situation?

Back

The situation can be represented by the inequality: 1.5c + 0.75b ≤ 75, where c is the number of color fliers and b is the number of black and white fliers.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

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 a solution.

Front

What does it mean for a solution to be 'reasonable' in the context of a problem?

Back

A reasonable solution is one that satisfies all constraints of the problem, such as budget limits or minimum requirements.