Number of solutions

Front

What is the definition of 'no solution' in equations?

Back

'No solution' means that there are no values for the variable that can satisfy the equation.

Front

What does it mean if an equation has 'one solution'?

Back

'One solution' means there is exactly one value for the variable that makes the equation true.

Front

What is an 'infinite solution' in the context of equations?

Back

'Infinite solutions' means that there are countless values for the variable that satisfy the equation, often seen in identities.

Front

If an equation simplifies to a false statement like '2 + 3 = 6', what type of solution does it have?

Back

It has 'no solution'.

Front

How do you determine if an equation has 'no solution'?

Back

If simplifying the equation leads to a contradiction, such as 'a = b' where a and b are different, it has no solution.

Front

What is the first step in solving the equation 4(8n - 1) = 19 + 32n?

Back

Distribute the 4 on the left side: 32n - 4 = 19 + 32n.

Front

What happens when you have the same variable on both sides of an equation?

Back

If the coefficients are equal and the constants are not, the equation has 'no solution'.

Front

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

Back

It indicates that the equation has 'infinite solutions'.

Front

In the equation -2(-4x + 7) = -2 + 4x, what is the first step to solve it?

Back

Distribute -2 on the left side: 8x - 14 = -2 + 4x.

Front

What is the result of the equation -4(3x + 2) = 3(-4x + 5) after simplification?

Back

It simplifies to a contradiction, indicating 'no solution'.