Modeling Equations (variables on both sides)

Front

What is a variable in an equation?

Back

A symbol, often represented by a letter, that stands for a number that can change or vary.

Front

What does it mean to model an equation?

Back

To create a mathematical representation of a real-world situation using variables and constants.

Front

What is the purpose of balancing an equation?

Back

To ensure that both sides of the equation represent the same value, maintaining equality.

Front

What does it mean to have variables on both sides of an equation?

Back

It means that the equation contains variables (like x) on both the left and right sides, which can be solved to find the value of the variable.

Front

How do you isolate a variable in an equation?

Back

By performing inverse operations to get the variable alone on one side of the equation.

Front

What is the first step in solving an equation with variables on both sides?

Back

Combine like terms and move all variable terms to one side of the equation.

Front

What is the equation for the model: 5x + 1 = 3x + 5?

Back

To solve, subtract 3x from both sides: 2x + 1 = 5, then subtract 1: 2x = 4, and finally divide by 2: x = 2.

Front

What is the equation for the model: 2x - 4 = x - 7?

Back

To solve, subtract x from both sides: x - 4 = -7, then add 4: x = -3.

Front

What is the equation for the model: 6x + 5 = 15?

Back

To solve, subtract 5 from both sides: 6x = 10, then divide by 6: x = 10/6 or x = 5/3.

Front

What is the equation for the model: 2x + 2 = -3x + 7?

Back

To solve, add 3x to both sides: 5x + 2 = 7, then subtract 2: 5x = 5, and divide by 5: x = 1.