Unit 1: Linear Equations and Inequalities

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

What does it mean if a linear equation has no solution?

Back

It means that there are no values of the variable that can satisfy the equation. For example, x + 6 = x has no solution.

Front

What does it mean if a linear equation has infinitely many solutions?

Back

It means that there are countless values of the variable that can satisfy the equation. For example, x + 6 = x + 6 has infinitely many solutions.

Front

How do you solve the inequality 2n + 4 < 16?

Back

Subtract 4 from both sides to get 2n < 12, then divide by 2 to find n < 6.

Front

What is the solution to the inequality 3x - 5 > -26?

Back

Add 5 to both sides to get 3x > -21, then divide by 3 to find x > -7.

Front

What is the solution to the inequality 3(k-5) + 9k ≥ -3?

Back

Distribute to get 3k - 15 + 9k ≥ -3, combine like terms to find 12k ≥ 12, then divide by 12 to find k ≥ 1.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

Front

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

Back

The symbol '>' means 'greater than'. For example, x > 5 means x is any number greater than 5.

Front

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

Back

The symbol '<' means 'less than'. For example, x < 3 means x is any number less than 3.

Front

What is the graph of the inequality n < 6?

Back

The graph is a number line with an open circle at 6 and a line extending to the left.