No Solution/Infinite Solution/One Solution

Front

What does it mean if an equation has one solution?

Back

An equation has one solution when there is exactly one value of the variable that satisfies the equation.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there is no value of the variable that can satisfy the equation.

Front

What does it mean if an equation has infinitely many solutions?

Back

An equation has infinitely many solutions when any value of the variable satisfies the equation.

Front

Example of an equation with one solution: Solve for n: −16 + 5n = −7(−6 + 8n) + 3

Back

n = 1.

Front

Example of an equation with no solution: Solve for x: -4(3x + 2) = 3(-4x + 5)

Back

No solution.

Front

Example of an equation with infinitely many solutions: Solve for x: 3x + 15 = 3(x + 5)

Back

Infinitely many solutions.

Front

What is the first step to determine the number of solutions of an equation?

Back

Simplify both sides of the equation.

Front

What is a contradiction in an equation?

Back

A contradiction occurs when simplifying an equation leads to a false statement, indicating no solution.

Front

What is an identity in an equation?

Back

An identity occurs when simplifying an equation leads to a true statement for all values of the variable, indicating infinitely many solutions.

Front

How can you tell if an equation has one solution?

Back

If, after simplification, you get a true statement with a specific value for the variable.