Solving Equations with Variable on Both Sides

Front

What is an equation with variables on both sides?

Back

An equation that contains variables on both the left and right sides, requiring manipulation to isolate the variable.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, 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 46 - 8p = 19 + p?

Back

The first step is to get all terms involving p on one side and constant terms on the other side.

Front

Solve: 46 - 8p = 19 + p

Back

p = 3

Front

What does it mean to combine like terms in an equation?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power.

Front

How do you solve the equation 14y + 5 = 8y - 1?

Back

First, subtract 8y from both sides, then subtract 5 from both sides to isolate y.

Front

Solve: 14y + 5 = 8y - 1

Back

y = -1

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a parenthesis.

Front

Solve: 5(3n + 10) = 40n

Back

n = 2

Front

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

Back

Checking your solution ensures that the value satisfies the original equation, confirming it is correct.