Multi-step Equations

Front

What is a multi-step equation?

Back

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

Front

What is the first step in solving the equation 2x - 3 + 4x = 27?

Back

Combine like terms: 2x + 4x = 6x, so the equation becomes 6x - 3 = 27.

Front

How do you isolate the variable in the equation 3(x - 1) = 2x + 9?

Back

First, distribute: 3x - 3 = 2x + 9. Then, subtract 2x from both sides: x - 3 = 9. Finally, add 3 to both sides: x = 12.

Front

What does it mean to simplify an expression?

Back

To simplify an expression means to combine like terms and perform operations to reduce it to its simplest form.

Front

What is the solution to the equation x/3 + 10 = 15?

Back

To solve, subtract 10 from both sides: x/3 = 5. Then, multiply both sides by 3: x = 15.

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 each term inside a parenthesis.

Front

How do you check if x = 1 is a solution for the equation 5x - 2 = 3?

Back

Substitute x = 1 into the equation: 5(1) - 2 = 3. This simplifies to 5 - 2 = 3, which is true.

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

What is the solution to the equation 3(x - 1) = 2x + 9?

Back

The solution is x = 12.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there is no value for the variable that makes the equation true.