Solving Equations with 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 solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

What are variables in an equation?

Back

Variables are symbols (like x, y, or f) that represent unknown values in mathematical expressions or equations.

Front

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

Back

It means that the variable appears in expressions on both sides of the equality sign, requiring manipulation to isolate the variable.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What is the first step in solving the equation f - 4 = 6f + 26?

Back

The first step is to move all terms involving f to one side and constant terms to the other side.

Front

Solve for f: f - 4 = 6f + 26

Back

f = -6

Front

What is the solution to the equation 7x - 4 = 3 + 8x?

Back

x = -7

Front

How do you check if your solution to an equation is correct?

Back

You substitute the solution back into the original equation to see if both sides are equal.

Front

What is the solution to the equation 5x - 14 = 8x + 4?

Back

x = -6