College Algebra Section 1.2

Linear Equations

Objectives of this Section

• Solve a Linear Equation

• Solve Rational Equations

• Solve Applied Problems Involving Linear Equations

The set of all values of a variable that make an equation a true statement are called solutions, or roots, of the equation.

We solve equations by creating a series of equivalent equations, that is equations that have precisely the same solution set.

Remember to solve by graphing either, Remember to solve by graphing either, make one side of the equation to 0 and look make one side of the equation to 0 and look for the x-intercepts orfor the x-intercepts or

Graph both sides of the equation on the Graph both sides of the equation on the same graph and look for where they same graph and look for where they intersectintersect

Example: Solve

8x + 58x + 5 = = 4x – 34x – 3 10x – 7 5x+710x – 7 5x+7

Steps for Setting Up Applied Problems

Step 1: Read the problem carefully, perhaps two or three times. Identify what you are looking for.Step 2: Assign a letter (variable) to represent what you are looking for. Express any remaining unknown quantities in terms of that variable.

Step 3: Make a list of known facts and translate them into mathematical expressions. These may take the form of an equation or later, an inequality.

Step 4: Solve the equation for the variable and answer the question using a sentence.Step 5: Check your answer with the facts of the problem.

Example: Yolanda, Mary, and Sophie won $200,000 playing the lottery. Based on how much each contributed to buy the ticket, Mary gets four fifths of what Yolanda gets, while Sophie gets three fourth of what Mary gets. How much does each receive?

y: amount received by Yolandam: amount received by Marys: amount received by Sophie

y m s 200000

y m s 200000

m y45

s m34

34

45y 3

5y

y y y 45

35

200000

125

200000y

y $83, .333 33

m 45

333 33 666 67($83, . ) $66, .

s 35

333 33 000($83, . ) $50,

assignment

Page 109: 1-8 all, 9-75 odds, 95-101 oddsPage 109: 1-8 all, 9-75 odds, 95-101 odds