Solving Equations with Variable on Both Sides

Front

What is an equation with variables on both sides?

Back

An equation that has variables (like x or y) 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, you perform inverse operations (addition, subtraction, multiplication, division) to both sides of the equation until the variable is alone on one side.

Front

What is the first step in solving the equation 4k + 39 = 7k + 6?

Back

Subtract 4k from both sides to begin isolating k.

Front

Solve: 4k + 39 = 7k + 6. What is k?

Back

k = 11.

Front

What is the purpose of combining like terms in an equation?

Back

Combining like terms simplifies the equation, making it easier to solve for the variable.

Front

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

Back

Subtract 8y from both sides and then isolate y to find y = -1.

Front

What does it mean to check your solution in an equation?

Back

It means substituting your solution back into the original equation to verify that both sides are equal.

Front

Solve: 6a = 60 + 36a. What is a?

Back

a = -2.

Front

What is the distributive property in solving equations?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a term across a sum or difference.

Front

How do you apply the distributive property to 5(3n + 10)?

Back

You multiply 5 by both 3n and 10 to get 15n + 50.