Solving Multi-Step Equations with Variables on Both Sides

Front

What is a multi-step equation?

Back

An equation that requires more than one step to solve, often involving operations like addition, subtraction, multiplication, and division.

Front

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

Back

It means that the variable(s) appear on both the left and right sides of the equation, requiring manipulation to isolate the variable.

Front

What is the first step in solving the equation 4(a + 3) = -32?

Back

Distribute 4 to both a and 3.

Front

How do you isolate a variable in an equation?

Back

By performing inverse operations to both sides of the equation until the variable is alone on one side.

Front

What is the distributive property?

Back

A property that states a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a set of parentheses.

Front

Solve for a: 4(2a + 3) = -3(a - 1) + 31

Back

a = 2.

Front

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

Back

x = -6.

Front

How do you combine like terms in an equation?

Back

By adding or subtracting coefficients of the same variable.

Front

What is the solution to the equation 6x + 5 = 10 + 5x?

Back

x = 5.

Front

What is the first step in solving the equation 2a - 4(a - 5) = 10?

Back

Distribute -4 to a and -5.