Modeling Equations (variables on both sides)

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables.

Front

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

Back

It means that the equation contains variables (like x or n) 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

To isolate a variable, you perform operations (like addition, subtraction, multiplication, or division) 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

The first step is to simplify both sides of the equation if possible, and then move all terms containing the variable to one side.

Front

Solve for x: 3x + 5 = 2x + 10

Back

x = 5

Front

Solve for n: 4n - 6 = 7n + 9

Back

n = -5

Front

What is the solution to the equation: 2x + 1 = x + 3?

Back

x = 2

Front

What does it mean to 'balance' an equation?

Back

Balancing an equation means ensuring that both sides of the equation remain equal after performing operations.

Front

If 5x - 3 = 2x + 12, what is x?

Back

x = 5

Front

What is the purpose of checking your solution in an equation?

Back

Checking your solution ensures that the value you found satisfies the original equation.