Chapter 2 Notes Algebra 1 name per

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1 Chapter 2 Notes Algebra 1 name per 1-STEP EQUATIONS Ex b = -3 Ex. 2 1.) Use the inverse operation to isolate the variable 2.) Check answer Ex. 3 Ex. 4 2-STEP EQUATIONS Ex 1. 3f 7 = 5 Ex 2. *Isolate the variable 1.) +/- the term w/out the variable to/from both sides of the =. 2.) m/d the coefficient by both sides of the =. *If top of fraction has a variable, Ex 3: c - 4 = 9 Ex x = 10 Multiply both sides by the -6 4 denominator, isolate variable MULTI-STEP EQUATIONS Ex 1: 2c + c +12 =78 Ex 2: 8(x + 2-1/4x) = 46 1.) Clear any fractions/decimals 2.) Distribute if necessary 3.) Combine Like Terms (CLT) 4.) solve using algebra rules *Check your answer

2 EQUATIONS VARIABLES Ex 1.: 6x + 3 = 8x -21 Ex. 2.: ½ (10h 8)+3h = ¼ ( h) ON BOTH SIDES 1.) Clear any fractions/decimals 2.) Distribute if necessary 3.) Combine Like Terms (CLT) 4.) Isolate the variable by +/- until the variables are one side and the constants on the other 5.) m/d your final step *Check your answer 1.) Solve accordingly IDENTITIES : sameness Left and Right side equal each other. Ex. 1: 4 4y = -2(2y 2 ) 1.) Solve accordingly NO SOLUTIONS : if no value of the variable makes the equation true Ex 2: 9 + 5n = 5n -1

3 FRACTION BUSTERS Ex. 1: Can only be used in equations Solve not expressions. 1.) Find LCM of ALL denominators Smallest number that each denom. can be divided into. 2.) Multiply the LCM by every term on both sides of the equation Ex. 2 Solve *** Fractions should be cleared or you made an error. 3.) Now solve!!!! 4.) Check DECIMAL BUSTERS Ex. 1 Solve Can only be used in equations not expressions. 1.) Find the term with the MOST decimal places.. 2.) Move the decimal in EVERY term that number of places. Add zeros for place value when needed. Ex. 2 Solve

4 TRANSFORMING FORMULAS Ex. 1 Solve for h Ex. 2 Solve for b 1.) Solve for the variable given. You can move other variables like # s You can multiply by the reciprocal the Ex. 3 Solve for f BEFORE distributing when that s on one side alone! PROPORTIONS An equation that states that two ratios are equal 2 ways to solve FRACTION BUSTER Ex. 4 CROSS MULTIPLY Ex. 5 MULTI-STEP Ex. 6 PROPORTIONS Use fraction busters or cross multiplying then solve for x. Use ( ) to show distribution!!!!

5 WORD PROBLEMS Ex. 1: You want to by one pair of pants and several pairs of socks. The pants AND EQUATIONS Cost $24.94 and the socks are $5.95 per pair. How many pairs of socks can 1, 2 or MULTISTEP EQUATIONS you buy if you have $50.00 to spend? 1.) Read checking for alg.expressions whole values and totals CLUE: solve without equation then write equation in the opposite direction than you solved MULTISTEP in which there 2 Ex. 1A: The attendance at a baseball game was 400 people. Student tickets unknown quantities cost $2 and adult ticks cost $3. Total ticket sales were $1050. How many 1.) Read tickets of each type were sold? 2.) Define unknowns to help come up with a plan. 3.) Write to total, if provided and write the equation backwards. Pg. 84 VAR. ON BOTH SIDES Ex 2: You can buy skates for $40, or you can rent some. Either way, you must Or, equals, same etc. rent safety equipment. How many hours must you skate before the cost of 1.) Set situations in w.p. equal to buying renting are the same? each other. Rental: skates & safety equipment is $3.50/hr 2.) solve Buy: Safety equipment: $1.50/hr and $40 for skates Equation h = 3.5h

6 Pg 100 USING FORMULAS Ex 3: The length of a rectangle is 4 in. greater than the width. The perimeter 1.) Read Of the rectangle is 24 in. find the dimensions of the rectangle 2.) draw a sketch 3.) write the required formula 4.) plug in given information 5.) Solve 6.) plug in to solve for desired answer Pg. 100CONSECUTIVE INTEGERS Ex 4: Find three consecutive integers whose sum is ) let n = 1 st unknown integers 2.) let n + 1 = the 2 nd number Etc. paying attention to key Words like even, odd,every other. 3.) solve 4.) plug in unknown value to find Consecutive numbers DISTANCE= (RATE) (TIME) SAME DIRECTION 1.) Read to determine type of Ex 5: A passenger train s speed is 60 mph and a freight trains speed is problem. 40 mi/hr. The passenger train travels the same distance in 1.5h less time than 2.) Set up chart to match formula The freight train. How long does each train take to make the trip? 3.) Fill in chart using variable for unknown quantity 4.) Fill in chart for 2 nd item using variable from 1 st train to create algebraic expressions you will use in equation Equation: 5.) Write equation setting trains equal to each other. 6.) Solve for unknown quantity 7.) plug in to find 2 nd unknown

7 1.) Read ROUND TRIP 2.) Define known and unknown Ex 6: On his way to work, your uncle averaged only 20 miles per hour. On his quantities. Drive home, he averaged 40 miles per hour. If the total time was 1 ½ hours, 3.) Make a chart How long did it take him to drive to work? 4.) Write an equation setting distances equal to each other. 5.) Solve for unknown 6.) Plug answer in where required to answer question. 1.) Read OPPOSITE DIRECTION 2.) Define unknowns set up chart Ex 7: At 10 am a car leaves a house at a rate of 60 mi/hr toward the library 3.) Fill in chart for 1 st unknown At the same rate, another car leaves the same house at a rate of 50 mi/hr in 4.) Fill in chart of 2 nd unknown the opposite direction. At what time will the cars be 330 miles apart? 5.) Write an equation 6.) Solve to answer question

8 Pg. 110 These involve combing MIXTURES 2 or more quantities. Ex 7: A store sells mixtures of almonds and cashes for $6.50 per pound. Almonds sell for $2.95 per pound and cashes sell for $7.95 per pound. How 1.) Read Many pounds of each should be used to make 80 pounds of this mixture? 2.) Define unknowns set up chart 3.) Fill in chart for 1 st unknown 4.) Fill in chart of 2 nd unknown 5.) Fill in chart for mixture total 6.) Write an equation setting the sum of the unknown quantities to total mixture. 7.) Solve to answer question PERCENT MIXTURES Ex 7: A solution is 30% chlorine and another solution is 60% chorine. How many liters of each solution should you use to make 120 liters of a solution That is 40% chlorine?

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