Number of Solutions

Front

What does it mean if an equation has an infinite number of solutions?

Back

It means that the equation is an identity, where any value of the variable satisfies the equation.

Front

What does it mean if an equation has no solution?

Back

It means that there is no value of the variable that can satisfy the equation, often resulting in a contradiction.

Front

What is an example of an equation with infinite solutions?

Back

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

Front

What is an example of an equation with no solution?

Back

An example is 2x + 3 = 2x + 5, which leads to a contradiction (3 = 5).

Front

What is the solution type for the equation 0 = 0?

Back

Infinite solutions (identity).

Front

What is the solution type for the equation -6 = 6?

Back

No solution.

Front

What is the solution type for the equation 2(4x + 3) = 8(x + 2) - 10?

Back

Infinitely many solutions.

Front

What is the solution type for the equation 3 = 1/3?

Back

No solution.

Front

What is the first step in solving a linear equation?

Back

Isolate the variable on one side of the equation.

Front

What does it mean for two equations to be equivalent?

Back

They have the same solution set.