Regents Review 2 Equations What type of

Regents Review #2 Equations

What type of Equations do we need to solve? 1) 2) 3) 4) 5) Simple Equations with Fractions Quadratic Equations Literal Equations (solving for another variable) Equations that help us solve word problems

Simple Equations ½ (2 x – 10) = 5 x – (6 x + 9) x – 5 = 5 x – 6 x – 9 x – 5 = -x – 9 Always check solution(s) to any equation ½ (2 -2 – 10) = 5(-2) – (6 -2 + 9) 2 x = -4 ½ (-14) = -10 – (-3) -7 x = -2 = -7 It checks!

How do we solve Quadratic Equations? 1) x 2 = a Example: x 2 = 16 Take the square root of both sides x= x = 4 or x = {4, -4} 2) x 2 + bx + c = 0 Example: x 2 – 5 x + 6 = 0 Set all terms equal to zero (x – 2)(x – 3)= 0 Factor x – 2 = 0 x – 3 = 0 Set each factor equal to zero x=2 x = 3 Solve x = {2, 3}

Equations with Fractions There are two ways to “clear” fractions in Equations… 1) Multiply both sides of the equation by the LCD (Least Common Denominator) 2) Cross Multiply (only works for proportions )

Equations with Fractions Cross Multiplication (solving proportions) Check for solutions that will make the denominator equal to zero. x = {3, 1}

Equations With Fractions Multiplying by the LCD CHECK

Literal Equations When solving literal equations, isolate the indicated variable using inverse operations

Word Problems We can use equations to solve many different types of word problems. When solving a word problem, remember to… 1)Define all unknowns (set up “Let” statements) 2)Write an equation relating all unknowns 3)Solve the equation 4)Determine the value of all unknowns 5)Answer the question (use appropriate units)

Word Problems Find two consecutive integers whose sum is -35. x: 1 st consecutive integer -18 x + 1: 2 nd consecutive integer -17 (-18 + 1) Remember: Consecutive integers count by 1’s Ex: x, x+1, x+2, x+3…. Consecutive odd or even integers count by 2’s Ex: x, x+2, x+4, x+6…

Word Problems Ticket sales for a music concert totaled $2, 160. Three times as many tickets were sold for the Saturday night concert than the Sunday afternoon concert. Two times as many tickets were sold for the Friday night concert than the Sunday afternoon concert. Tickets for all three concerts sold for $2 each. Find the number of tickets sold for the Saturday night concert. x: number of tickets sold for the Sunday concert 180 tickets 3 x: number of tickets sold for the Saturday concert 540 tickets 3(180) 360 tickets 2(180) 2 x: number of tickets sold for the Friday concert 2 x + 2(3 x) + 2(2 x) = 2160 2 x + 6 x + 4 x = 2160 12 x = 2160 x = 180 There were 540 tickets sold for the Saturday night concert

Word Problems A person has 23 coins made up of dimes and quarters worth $3. 35. How many coins of each type are there? COIN QTY VALUE($) Dimes x . 10 x Quarters 23 – x . 25(23 – x) 0. 10 x + 0. 25(23 – x) = 3. 35 10 x + 25(23 – x) = 335 10 x + 575 – 25 x = 335 -15 x + 575 = 335 -15 x = -240 x = 16 16 dimes 7 quarters (23 – 16) Check 7(25) + 16(10) = 335 175 + 160 = 335

Word Problems The area of a rectangle is 120 square inches. If the length is two more than the width, find the dimensions of the figure. A = lw The width is 10 inches 120 = (x + 2)(x) The length is 12 inches Length: x + 2 120 = x 2 + 2 x – 120 0 = (x + 12)(x – 10) x + 12 = 0 x – 10 = 0 x = -12 x = 10 Reject Width: x

Word Problems Distance, Rate, Time (D = RT) Two Options 1) Finding Rate 2) Finding Time How do you know what to look for? Distance: How far? Rate: How fast? Time: How long? D R T

Word Problems Hannah took a trip to her cousin’s house. She drove 120 miles to get there. If it took her 1. 2 hours to get halfway to her cousin’s house, what was her average rate of speed? Important Information: Time: 1. 2 hours Distance traveled: 60 miles (120/2) Rate: ? If Hannah decided to travel 10 mph faster on the way home, how long would it take her?

Now it’s your turn to review on your own! Using the information presented today and your review packet, complete the practice problems in the packet. Regents Review #3 is FRIDAY, May 17 th BE THERE!!!!