Multi-step Equations

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.

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.

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.

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.

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

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

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

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

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

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