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 does it mean to isolate a variable in an equation?

Back

Isolating a variable means rearranging the equation so that the variable is on one side of the equation by itself, making it easier to solve.

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 two or more terms inside a set of parentheses.

Front

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

Back

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

Front

What is a variable in an equation?

Back

A variable is a symbol, often a letter, that represents an unknown number in an equation.

Front

How do you write an equation from a word problem?

Back

Identify the quantities involved, assign variables to unknowns, and translate the relationships described in the problem into mathematical expressions.

Front

What is the first step in solving the equation 15x - 37 = 38?

Back

Add 37 to both sides to isolate the term with the variable: 15x = 75.

Front

How do you find the total cost in a rental problem?

Back

Add the fixed cost to the variable cost, which is calculated by multiplying the rate per unit by the number of units used.

Front

If Bobbie paid $415 for internet, how do you find the number of months she paid?

Back

Set up the equation: 100 + 35m = 415. Subtract 100 from both sides: 35m = 315. Then divide by 35: m = 9.

Front

What is the equation for the cost of renting a car at Joe's Clown Car Rental Agency?

Back

The equation is 105 = 0.75x + 35, where x is the number of miles driven.