Linear Inequalities Review

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 (>, <, ≥, ≤) instead of an equal sign.

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 is either greater than or equal to the value on the right.

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 is either less 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 region that satisfies the inequality.

Front

What is the standard form of a linear inequality?

Back

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

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, then the point is a solution.

Front

What is the difference between 'less than' and 'less than or equal to' in inequalities?

Back

'Less than' (<) means the value cannot equal the number, while 'less than or equal to' (≤) means the value can equal the number.

Front

Write the linear inequality for the situation: A landscaper wants to spend less than $1000 on trees and bushes costing $14 and $5 respectively.

Back

14x + 5y < 1000, where x is the number of trees and y is the number of bushes.

Front

Write the linear inequality for the situation: A team wants to make at least $240 selling drinks for $1 and $2 each.

Back

x + 2y ≥ 240, where x is the number of $1 drinks and y is the number of $2 drinks.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality.