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 isolate the variable and solve for its value.

Front

How do you solve the equation 8v - 4(v + 8) = 8?

Back

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

Front

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

Back

The first step is to distribute the 2 to both terms inside the parentheses: 3x + 8x - 8 = 3.

Front

What is the solution to the equation -(n - 8) = -2?

Back

To solve, 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

How do you isolate a variable in a multi-step equation?

Back

To isolate a variable, perform inverse operations in the reverse order of operations: start with addition/subtraction, then multiplication/division.

Front

What does it mean to combine like terms in an equation?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power to simplify the equation.

Front

What is the solution to the equation -19 = -8(-4 + a) - (2a + 1)?

Back

First, distribute: -19 = 32 - 8a - 2a - 1. Combine like terms: -19 = 31 - 10a. Subtract 31 from both sides: -50 = -10a. Finally, divide by -10 to find a = 5.

Front

What is the importance of checking your solution in a multi-step equation?

Back

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

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 two or more terms inside a set of parentheses.

Front

How do you handle equations with variables on both sides?

Back

To solve equations with variables on both sides, first move all variable terms to one side and constant terms to the other side.