Number of Solutions

Front

What does the equation 4=4 represent in terms of solutions?

Back

It represents an infinite number of solutions, indicating that the equation is an identity.

Front

What is the first step to solve for b in an equation like 5b - 6 = 4?

Back

Add 6 to both sides of the equation.

Front

After adding 6 to both sides of 5b - 6 = 4, what is the next step?

Back

Divide both sides by 5.

Front

How do you determine if a given value is a solution to an equation?

Back

Substitute the value into the equation and check if both sides are equal.

Front

For the equation 15 + m = 28, is m = 13 a solution?

Back

Yes, because substituting 13 for m gives 15 + 13 = 28, which is true.

Front

What is the solution to the equation 5h - 6 - h + 10 = 12?

Back

h = 2.

Front

What does the equation x + 9 = x - 9 imply about the number of solutions?

Back

It implies there is no solution, as the equation simplifies to a false statement.

Front

What is an identity in the context of equations?

Back

An identity is an equation that is true for all values of the variable.

Front

What is a contradiction in the context of equations?

Back

A contradiction is an equation that has no solutions, as it leads to a false statement.

Front

What is the general form of a linear equation in one variable?

Back

The general form is ax + b = c, where a, b, and c are constants.