Multi-Step Linear Equations

Front

What is a multi-step linear equation?

Back

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

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you solve the equation 6(2x + 1) = 18?

Back

1. Distribute: 12x + 6 = 18. 2. Subtract 6 from both sides: 12x = 12. 3. Divide by 12: x = 1.

Front

What does it mean to isolate a variable?

Back

Isolating a variable means to manipulate an equation so that the variable is on one side of the equation by itself.

Front

What is the first step in solving the equation 2x + 3(5x - 7) = 47?

Back

The first step is to distribute the 3: 2x + 15x - 21 = 47.

Front

What is a solution to an equation?

Back

A solution to an equation is a value that, when substituted for the variable, makes the equation true.

Front

How do you check if x = 4 is a solution to the equation 2x + 3(5x - 7) = 47?

Back

Substitute x = 4 into the equation: 2(4) + 3(5(4) - 7) = 8 + 3(20 - 7) = 8 + 39 = 47, which is true.

Front

What is the solution to the equation 3x - 5 = -26?

Back

x = -7.

Front

How do you solve the equation X/7 - 4 = -5?

Back

1. Add 4 to both sides: X/7 = -1. 2. Multiply both sides by 7: X = -7.

Front

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

Back

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