# MATH 111 Lecture Notes - Lecture 1: Memory Stick, Cross Product, American Broadcasting Company

by OC2615361

This

**preview**shows pages 1-2. to view the full**7 pages of the document.**1.) Linear Equations- Solve 1.1, 8/20/2018

-3(w-4)+5=10-(w+1) w=unknown (distribute)

If it has an equal sign we know it is an equation and we solve equations.

-3w+12+5=10-(w+1) (distribute)

-3w+12+5=10-w-1 (simplify)

-3w+17=9-w (move the variable to the same side)

-2w+17=9 (move all the numbers to the same side)

-2w=-8

W=4 (Check)

Ex.) Solve-

(m-2)/5-(m-4)/2=(m+5)/15+2 (linear because the variable isn’t in the denominator)

30 (m-2/5 – m-4/2)= 30 (m+5/15 +2)

30×(m-2)/5-30×(m-4)/2=30 (m+5)/15+30x2

6(m-2)-15(m+4)=2m+5+6(2)

Then distribute, combine like terms, and simplify

6m-12-15m+60=2m+10+60 Always do the opposite of what we are doing to simplify things

-9m+48=2m+70

-11m+48=70

-11m=22

M=-2 (Check)

Ex. A couple needs to decide whether to buy a used car for $8,000 or lease a new car for an

initial down payment of of $2,500 followed by 36 monthly payments of $225.

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

A.) Write a model for the cost C in dollars to lease the car for T months.

C= 2,500+225(T)

B.) After how many months will the cost to lease the new car be equal to the cost to buy a used

car?

+=# of months

2500+225T= 8800

225T=6300

T=28 months

2. Solving Rational Equations *rational bc X is in the denominator

Ex. Solve- *checking is mandatory here

12/x=6/2x+3

12/x=6/2x+3

12/x=3/x+3

12/x-3/x=3

9/x=3/1 *cross multiply (cross product a/b=c/d)

Ad=bc

9(1)=3x

X=3 (check)

Ex. Solve and Check

x/(x-4)=4/(x-4)-4⁄5 (factored?) LCD= 5(x-4)

x/x-4=4/x-4- 4/5

5x/5(x-4)=20/5(x-4)-4(x-4)/5(x-4) LCD becomes the new denominator

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