Multi Step Equations with Variables on Both Sides

Front

What is a multi-step equation?

Back

A multi-step equation is an equation that requires more than one step to solve, often involving combining like terms, using the distributive property, and isolating the variable.

Front

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

Back

Having variables on both sides of an equation means that the variable appears on both the left and right sides, requiring manipulation to isolate the variable.

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 each term inside a parenthesis.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable alone on one side of the equation.

Front

What is the first step in solving the equation -1(n - 8) = -2?

Back

The first step is to distribute -1 to both terms inside the parentheses, resulting in -n + 8 = -2.

Front

How do you solve the equation 7 + a/3 = 5?

Back

Subtract 7 from both sides to get a/3 = -2, then multiply both sides by 3 to find a = -6.

Front

What is the solution to the equation 12k + 15 = 35 + 2k?

Back

First, subtract 2k from both sides to get 10k + 15 = 35, then subtract 15 from both sides to find 10k = 20, and finally divide by 10 to get k = 2.

Front

How do you solve for b in the equation 9b + 1 = 2b + 29?

Back

Subtract 2b from both sides to get 7b + 1 = 29, then subtract 1 from both sides to find 7b = 28, and divide by 7 to get b = 4.

Front

What is the solution to the equation 2/3(3x + 1/2) - 1/4 = 1/3?

Back

First, distribute 2/3 to both terms inside the parentheses, then combine like terms and isolate x to find x = 3/8.

Front

What does 'combining like terms' mean?

Back

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