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 false statement, 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. This is typically the case when the variable can be isolated to yield a single numerical answer.

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 the equation simplifies to a true statement, such as 0 = 0.

Front

Solve the equation: 6x + 9 – x = 3x + 9 + x

Back

No Solution

Front

Solve the equation: 8z - 22 = 3 (3z + 11) - z

Back

No Solution

Front

Solve the equation: 14 - 2(3p + 1) = 6(4 + p)

Back

One Solution

Front

Solve the equation: 5x + 6 = 2 + 3x

Back

One Solution

Front

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

Back

Infinite Solutions

Front

What is the first step in solving linear equations?

Back

The first step is to simplify both sides of the equation, if possible, by combining like terms.

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.