How Many Solutions Multi-Step Equations

Front

What is a multi-step equation?

Back

An equation that requires more than one step to solve, often involving combining like terms, using the distributive property, or isolating the variable.

Front

What does it mean if an equation has one solution?

Back

It means there is exactly one value for the variable that makes the equation true.

Front

What does it mean if an equation has no solution?

Back

It means there is no value for the variable that can satisfy the equation.

Front

What does it mean if an equation has infinitely many solutions?

Back

It means that any value for the variable will satisfy the equation, often resulting from equivalent expressions.

Front

How do you determine if an equation has no solution?

Back

If simplifying the equation leads to a false statement, such as 0 = 5, it has no solution.

Front

What is the first step in solving the equation -3x + 1 = x + 9 - 4x?

Back

Combine like terms on the right side to simplify the equation.

Front

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

Back

x = -2, which means the equation has one solution.

Front

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

Back

No matter what constant is substituted in for the variable, the equation will NEVER be true.

Front

What is the equation that models Cheryl's earnings if she gets paid $8 per hour and $15 for working late?

Back

8h + 15 = 96.

Front

What is the distributive property?

Back

A property that states a(b + c) = ab + ac, used to simplify expressions.