Linear Equations (Determine number of solutions/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 is no value of the variable that can satisfy the equation. For example, the equation 2x + 3 = 2x + 5 has no solution.

Front

What does it mean if a linear equation has one solution?

Back

It means there is exactly one value of the variable that satisfies the equation. For example, the equation x + 2 = 5 has one solution: x = 3.

Front

What does it mean if a linear equation has infinite solutions?

Back

It means that any value of the variable satisfies the equation. For example, the equation 2x + 4 = 2(x + 2) has infinite solutions.

Front

How do you determine the number of solutions for the equation 8z - 22 = 3(3z + 11) - z?

Back

First, simplify both sides. If you end up with a false statement (like 0 = 5), it has no solution. If you get a true statement (like 0 = 0), it has infinite solutions.

Front

What is an inequality?

Back

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

Front

How do you solve the inequality 3(x - 2) < 2(x + 9)?

Back

Distribute and simplify: 3x - 6 < 2x + 18. Then isolate x to find x < 24.

Front

What is the solution to the inequality 6x + 10 > 5x - 12?

Back

Isolate x: 6x - 5x > -12 - 10, which simplifies to x > -22.

Front

What does it mean if an inequality has no solution?

Back

It means that there is no value of the variable that can satisfy the inequality. For example, x > x has no solution.

Front

What is the solution to the equation 7 = 7?

Back

This equation has infinite solutions because it is always true for any value of the variable.