How Many Solutions

Front

What does it mean if an equation has no solution?

Back

It means that there are no values for the variable that can satisfy the equation. For example, the equation 4 = 8 has no solution.

Front

What is an example of an equation with infinitely many solutions?

Back

An example is the equation 2x + 3 = 2x + 3, which is true for all values of x.

Front

What does it mean if an equation has one solution?

Back

It means 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 is the first step in solving a linear equation?

Back

The first step is to isolate the variable on one side of the equation.

Front

How can you tell if two equations are equivalent?

Back

Two equations are equivalent if they have the same solution set.

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.

Front

What does it mean for an equation to be inconsistent?

Back

An inconsistent equation is one that has no solution, such as 2x + 3 = 2x + 5.

Front

What is the solution to the equation 5x - 2 = 3x + 6?

Back

The solution is x = 4.

Front

What does it mean if an equation simplifies to a true statement like 0 = 0?

Back

It means the equation has infinitely many solutions.

Front

What is the solution to the equation 3x + 4 = 3x - 2?

Back

The solution is none; this equation has no solution.