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 make the expression as concise as possible.

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

1. Distribute -4: -4 - 12x = 68. 2. Add 4 to both sides: -12x = 72. 3. Divide by -12: x = -6.

Front

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

Back

1. Distribute -6: 30 - 30r + 3r = -69. 2. Combine like terms: 30 - 27r = -69. 3. Subtract 30: -27r = -99. 4. Divide by -27: r = -1.

Front

What does it mean to combine like terms?

Back

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

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 isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable alone on one side of the equation.

Front

What is the first step in solving a multi-step equation?

Back

The first step is often to simplify both sides of the equation by distributing and combining like terms.

Front

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

Back

1. Distribute 2: 6 - 6x + 8. 2. Combine like terms: 14 - 6x.