Multi-Step Equations with Rational Numbers

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 does it mean to simplify an expression?

Back

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

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 set of parentheses.

Front

How do you solve the equation -4(1 + 3x) = 68?

Back

First, distribute -4: -4 - 12x = 68. Then, add 4 to both sides: -12x = 72. Finally, divide by -12: x = -6.

Front

What is a rational number?

Back

A rational number is any number that can be expressed as a fraction a/b, where a and b are integers and b is not zero.

Front

How do you combine like terms?

Back

To combine like terms, add or subtract the coefficients of terms that have the same variable raised to the same power.

Front

What is the solution to the equation 6 + 2(-3x + 4)?

Back

The solution is 14 - 6x after simplifying the expression.

Front

What does it mean to isolate a variable?

Back

To isolate 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 -6(-5r + 6) + 3r = -69?

Back

The first step is to distribute -6: 30r - 36 + 3r = -69.

Front

What is the final solution for r in the equation -6(-5r + 6) + 3r = -69?

Back

The final solution is r = -1.