Solving 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, involving operations such as addition, subtraction, multiplication, and division to isolate the variable.

Front

How do you isolate a variable in a linear equation?

Back

To isolate a variable, perform inverse operations to both sides of the equation until the variable is alone on one side.

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 solve the equation 38 + 7k = 8(k + 4)?

Back

First, distribute the 8: 38 + 7k = 8k + 32. Then, subtract 7k from both sides: 38 = k + 32. Finally, subtract 32 from both sides to find k = 6.

Front

What is the first step in solving the equation 8v - 4(v + 8) = 8?

Back

The first step is to distribute -4 to both terms inside the parentheses: 8v - 4v - 32 = 8.

Front

What does it mean to combine like terms?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power to simplify an expression.

Front

How do you solve the equation -(n - 8) = -2?

Back

First, distribute the negative sign: -n + 8 = -2. Then, subtract 8 from both sides: -n = -10. Finally, multiply by -1 to find n = 10.

Front

What is the solution to the equation 3(x - 2) = 18?

Back

First, distribute the 3: 3x - 6 = 18. Then, add 6 to both sides: 3x = 24. Finally, divide by 3 to find x = 8.

Front

What is the importance of checking your solution in a linear equation?

Back

Checking your solution ensures that the value you found satisfies the original equation, confirming that it is correct.

Front

What is an inverse operation?

Back

An inverse operation is an operation that reverses the effect of another operation, such as addition and subtraction or multiplication and division.