Number of Solutions

Front

What is the definition of 'One Solution' in an equation?

Back

An equation has 'One Solution' when there is exactly one value of the variable that satisfies the equation.

Front

What does 'No Solution' mean in the context of equations?

Back

'No Solution' means that there is no value of the variable that can satisfy the equation.

Front

Define 'Infinite Solutions' in an equation.

Back

An equation has 'Infinite Solutions' when any value of the variable satisfies the equation, meaning there are countless solutions.

Front

How do you determine if an equation has one, no, or infinite solutions?

Back

You can determine this by simplifying the equation and checking if it leads to a true statement, a false statement, or an identity.

Front

What is the first step in solving the equation -2(-4x + 7) = -2 + 4x?

Back

The first step is to distribute -2 on the left side of the equation.

Front

What is the result of simplifying the equation 3x - 8 = 3(x - 4) + 1?

Back

The result is 3x - 8 = 3x - 12 + 1, which simplifies to 3x - 8 = 3x - 11.

Front

What does it mean if after simplifying an equation, both sides are equal?

Back

If both sides are equal after simplification, the equation has infinite solutions.

Front

What is the significance of the coefficients in the equation 4(2x + 1) = 5x + 3x + 9?

Back

The coefficients determine the relationship between the variables and constants, which helps in identifying the number of solutions.

Front

How can you tell if an equation has no solutions?

Back

An equation has no solutions if simplifying leads to a contradiction, such as 0 = 5.

Front

What is the solution to the equation -2(3m + 6) = -3(4 + 2m)?

Back

The solution is infinite solutions, as both sides simplify to the same expression.