Solving Equations with Variable 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 is a variable in mathematics?

Back

A variable is a symbol, often a letter, that represents an unknown value in an equation or expression.

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 an equation with variables on both sides?

Back

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

Front

Solve: 6a = 60 + 36a

Back

a = -2

Front

Solve: 8b + 10 = 3b + 25

Back

b = 3

Front

Solve: 4(w + 3) = 2(5w + 6)

Back

w = 0

Front

Solve: 45m - 38 = 5m - 158

Back

m = -3