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 Dependent Variable

 Number of inequalities to solve: 23456789
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# 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. A · student · solves · the · literal · equation · · for · the · variable · P. ·The · student's · answer  ·  is · · is · this · a · correct · response? · Explain. A · tutor · states · that · the · formula · · can · also · be · expressed · as .· · Do · you · agree? 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 unknowns1. 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 noon. After 3 hours they are 60 miles apart. If one boat travels twice as fast as the other, find the average rate of each boat. 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 mph. Since they are 60 miles apart after 3 hours, the difference in the distance traveled by the faster boat B and the slower boat A is 60 miles. distance traveled by B – distance traveled by A = 60 (average rate of B)(time) – (average rate of A)(time) = 60 The average rates are 20 mph and 40 mph