Number of solutions

Front

What is the definition of a solution in algebra?

Back

A solution is a value or set of values that satisfies an equation.

Front

What does it mean if an equation has one solution?

Back

It means there is exactly one value for the variable that makes the equation true.

Front

What does it mean if an equation has no solution?

Back

It means there is no value for the variable that can satisfy the equation.

Front

What does it mean if an equation has infinite solutions?

Back

It means there are an unlimited number of values for the variable that satisfy the equation, often indicating that the equations are equivalent.

Front

Example of an equation with one solution: x + 2 = 5. What is the solution?

Back

x = 3.

Front

Example of an equation with no solution: 2x + 3 = 2x + 5. What is the conclusion?

Back

No solution, because 3 cannot equal 5.

Front

Example of an equation with infinite solutions: 3(x + 2) = 3x + 6. What is the conclusion?

Back

Infinite solutions, because both sides are equivalent.

Front

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

Back

Simplify both sides of the equation as much as possible.

Front

How can you tell if an equation has no solution?

Back

If simplifying leads to a false statement, such as 0 = 5.

Front

How can you tell if an equation has infinite solutions?

Back

If simplifying leads to a true statement, such as 0 = 0.