Solving Multi-Step Equations (with Distributive Property)

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you solve the equation -3x + 1 = x + 9 - 4x?

Back

Combine like terms: -3x + 1 = -3x + 9. This simplifies to 1 = 9, which is a contradiction, indicating no solution.

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 on both sides.

Front

What is the first step in solving the equation 4 - 2(x - 3) = 24?

Back

Apply the Distributive Property: 4 - 2x + 6 = 24.

Front

What is the solution to the equation 3x + 15 = 3(x + 5)?

Back

This simplifies to 3x + 15 = 3x + 15, which is true for all x, indicating infinitely many solutions.

Front

How do you isolate the variable in the equation (2x - 3) / 4 = 9?

Back

Multiply both sides by 4 to eliminate the fraction: 2x - 3 = 36, then add 3 and divide by 2 to find x = 19.5.

Front

What is a multi-step equation?

Back

A multi-step equation requires more than one step to isolate the variable, often involving operations like addition, subtraction, multiplication, and division.

Front

What does it mean to solve for a variable?

Back

To solve for a variable means to find its value that makes the equation true.

Front

What is the solution to the equation 4 - 2(x - 3) = 24?

Back

The solution is x = -7.

Front

What is the goal of solving equations?

Back

The goal is to find the value of the variable that makes the equation true.