Pre-Algebra - Chapter 4 - Solving Equations/Equations

Steps for how to solve a Multi-Step Equation

1. Distribute, combine Like Terms 2. All variable terms on left side 3. Numbers on right 4. Solve the basic one-step equation

Examples for One-step Equations

1. x - 6 = -14 x - 6 = -14 +6 +6 ____________ x = -8 2. -3y = 30 ____ ___ -3 -3 ________________ y = -10

Examples for Multi-step Equations

1.1. -3 (x - 6) + 4 (x +1) = 7x - 10 -3x + 18 + 4x + 4 = 7x -1 0 1.2. x + 22 = 7x -10 1.3. x + 22 = 7x -10 -7x -22 -7x -22 ______________________ -6x = -32 1.4. -6x = -32 x = -32/-6 = 16/3 Note - the number 1 before variables is not written, only the variable is written. e.g. 1x = x.

Examples for Two-step Equations

1.1. 2/5m + 3 = 2 - 3 -3 _______________ 2/5m = -1 1.2. 5/2 * 2/5 = 5/2 * -1 = m = -5/2

Multi-step Equations

A Multi-step Equation is an equation in which you will need to do multi steps in order to find the answer to that equation. Although multi-step equations take more time and more operations, they can still be simplified and solved by applying basic algebraic rules.

One-step Equations

A One-step Equation is an equation in which you will only need to do one step in order to find the answer to that equation.

Two-step Equations

A Two-step Equation is an equation in which you will need to do two steps in order to find the answer to that equation.

Equations

A statement that the values of two mathematical expressions are equal (indicated by the sign =).

Formulas and Literal Equations

Sometimes you have a formula, such as something from geometry, and you need to solve for some variable other than the "standard" one. For instance, the formula for the perimeter P of a square with sides of length s is P = 4s. You might need to solve this equation for s, so you can plug in a perimeter and figure out the side length.This process of solving a formula for a given variable is called "solving literal equations".