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 6x - 4 = 8x?

Back

The first step is to get all terms involving the variable on one side of the equation. You can do this by subtracting 6x from both sides.

Front

What does it mean to isolate the variable in an equation?

Back

Isolating the variable means to manipulate the equation so that the variable is alone on one side, allowing you to find its value.

Front

How do you combine like terms in the equation 2x - 3 + 4x = 27?

Back

You combine like terms by adding the coefficients of the x terms: 2x + 4x = 6x.

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

Solve the equation 8v - 4(v + 8) = 8.

Back

First, distribute: 8v - 4v - 32 = 8. Then combine like terms: 4v - 32 = 8. Add 32 to both sides: 4v = 40. Finally, divide by 4: v = 10.

Front

What is the solution to the equation 2x + 3(5x - 7) = 47?

Back

First, distribute: 2x + 15x - 21 = 47. Combine like terms: 17x - 21 = 47. Add 21 to both sides: 17x = 68. Finally, divide by 17: x = 4.

Front

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

Back

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

Front

What is the solution to the equation 2x - 3 + 4x = 27?

Back

Combine like terms: 6x - 3 = 27. Add 3 to both sides: 6x = 30. Divide by 6: x = 5.

Front

What is the importance of understanding multi-step equations?

Back

Understanding multi-step equations is crucial for solving more complex algebraic problems and for developing critical thinking and problem-solving skills.