Math 111 Chapter 1 Sections 1 & 2 Reviews
MTH ·111·First ·day · Review
Name
Solve · and · check A · student · multiplies · each · side · of · the · equation · · · by · 2 · and · produces · the equation · · Has · the · student · produced · an · equivalent · equation ? · · Explain . 
3. Suppose we attempt to solve the equation 4x =
7x by first dividing each side of the equation by x. The result is 4 = 7, which is not true. Explain what happened.

Mth 111 Topics Chapter 1 Overview Section 1.1 Solving Linear Equations Solving Linear Equations involving distributive property and foil Solving literal equations Applications average, mixture, uniform motion, work Section 1.2 Solving quadratics: o by factoring and zero product principle; o square root; o completing the square; o quadratic formula; Discriminant Applications: square box, tossing an object 
Forming Equivalent Equations An equation can be rewritten into an equivalent form by: 1. Simplify either side 2. Using the Golden Rule of Algebra Do unto one side as thou hath done unto the other 3x = 7y equivalent to 3x + 5 = 7y + 5 3. Interchanging sides 
Linear Equations : A linear equation in a single variable x is an equation that can be written in the form ax + b = 0 where a and b are real numbers, with a not 0. Solve 
Solve

Literals Equations : formulas with several
unknowns 1. 10 = a  4x, solve for x 2. 8 = ax + 3x , solve for x 3. P = S  dt,
solve for t 
Word Problems 1. What do you need to know to solve the problem? Write this down in English. 2. Assign numbers to the known parts. Assign a letter to the unknown parts 3. Translate this into an algebraic equation or inequality. 4. Solve. 5. Make sure that your solution answers the original question 
Useful Formulas Business: Revenue = Profit  Cost Simple Interest : I = Prt Mixtures: (1st % × Amt) + (2nd % × Amt) = Final % × Amt Rate problems: Distance = rate × time Work Problems: (part done by A ) + (part done by B) = 1 whole job Averages: 
Applications: Averages: The average on your four tests is 91.25. Your test scores are 92, 86, and 98 with one test score gone missing. Find it! 
Simple Interest : I = Prt You invest part of a $10,000 bonus in a 2% simple interest account and the remainder of the money at 5% simple interest. Together the investments earn $400 per year. find the amount at each rate. let x be amount in 2% let 10000  x be amount in 5% t = 1 
Rate problems : Distance = rate × time
Example : Two boats traveling the same direction
leave a harbor at First we need to picture the situation. Let A be the slower boat and B be the faster one. Let x mph be the average rate of boat A. The
average rate of boat B is 2x
(average rate of B)(time) – (average rate of A)(time)
= 60 
The average rates are 20 mph and 40 mph 