## 6.6 Outline

- Introduction to problem solving
- principle of substitution
- procedure
- translating
- sum
- difference
- product
- quotient

- Number relationships
- formulate an equation
- consecutive integers

- Distance relationships
- Pythagorean relationships
- If two sides of a right triangle are know, the third can be found by using the Pythagorean theorem.
- If a right triangle has sides
*a*and*b*and hypotenuse*c*, then*a2*+*b2*=*c2*.

## 6.6 Essential Ideas

**PROCEDURE FOR PROBLEM SOLVING IN ALGEBRA
**

**Step 1:**Understand the problem. This means you must read the problem and note what it is about. Focus on processes rather than numbers. You cannot work a problem you do not understand. A sketch may help in understanding the problem.

**Step 2:**Devise a plan. Write down a verbal description of the problem using operation signs and an equal or inequality sign. Note the following common translations.

**Step 3:** Carry out the plan. In the context of word problems, we need to proceed deductively by carrying out the following steps.

**Choose a variable.** If there is a single unknown, choose a variable. If there are several unknowns, you can use the substitution property to reduce the number of unknowns to a single variable. Later we will consider word problems with more than one unknown.

**Substitute.** Replace the verbal phrase for the unknown with the variable.

**Solve the equation.** This is generally the easiest step. Translate the symbolic statement (such as *x* = 3) into a verbal statement. Probably no variables were given as part of the word problem, so *x* = 3 is not an answer. Generally, word problems require an answer stated in words. Pay attention to units of measure and other details of the problem.

**Step 4:** Look back. Be sure your answer makes sense by checking it with the original question in the problem. Remember to answer the question that was asked.