Multi-Step Equations: One, None, or Infinite Solutions

Front

What is a multi-step equation?

Back

A multi-step equation is an equation that requires more than one step to solve, often involving operations like addition, subtraction, multiplication, and division.

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when any value for the variable satisfies the equation, indicating that the two sides of the equation are equivalent for all values.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there is no value for the variable that can make the equation true, often resulting in a contradiction.

Front

What is the first step in solving the equation 3 + 5n = 5n + 3?

Back

The first step is to simplify both sides of the equation, which shows that both sides are equal, leading to infinite solutions.

Front

How do you determine if an equation has one solution?

Back

An equation has one solution if, after simplifying, you find a specific value for the variable that makes the equation true.

Front

Solve the equation: 8x + 38 = -3(-6 - 4x). What is the solution?

Back

The solution is x = -1.

Front

What is the significance of the equation -4(3x + 2) = 3(-4x + 5) having no solution?

Back

It indicates that the two sides of the equation represent parallel lines that never intersect.

Front

What does the equation 5y - 15 = 5(y - 2) illustrate about solutions?

Back

This equation illustrates that it simplifies to a true statement (0 = 0), indicating no solution.

Front

What is the solution to the equation -5(2x - 4) = 2(10 - 5x)?

Back

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

Front

What is the importance of checking your solution in multi-step equations?

Back

Checking your solution ensures that the value satisfies the original equation, confirming its correctness.