One Solution, No Solution, Infinite Solutions

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there are no values for the variable that can satisfy the equation. This often occurs when simplifying leads to a contradiction, such as 0 = 5.

Front

What does it mean if an equation has one solution?

Back

An equation has one solution when there is exactly one value for the variable that satisfies the equation. For example, the equation x + 2 = 5 has one solution: x = 3.

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when any value for the variable satisfies the equation. This occurs when both sides of the equation are equivalent after simplification, such as 2x + 4 = 2(x + 2).

Front

Solve: 2x + 1 = 2x - 1

Back

No Solution

Front

Simplify and determine the solution type: 3x - 7 = 3(x - 3) + 2

Back

Infinite Solutions

Front

Solve: 3(x-2) + 1 = 3x - 5

Back

Infinite Solutions

Front

Solve: 23 - 9x = -56x - 28

Back

x = -1.09

Front

Solve: 12(x + 3) = 4(2x + 9) + 4x

Back

Infinite Solutions

Front

What is a contradiction in an equation?

Back

A contradiction occurs when the simplification of an equation leads to an impossible statement, such as 0 = 5, indicating no solutions.

Front

What is the first step in solving a linear equation?

Back

The first step is to simplify both sides of the equation, which may involve distributing, combining like terms, or moving terms to one side.