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Name:_________________________ Algebra 1 Chapter 3 Test Review Solution Guide Period:________ Date:_____________ Solve each equation – No Decimals! 1. 3( x 5) 2 x 15 3x 15 2x 15 5x 15 15 5x 30 x6 2. 3. distribute the 3 combine like terms(3x + 2x) add 15 to both sides divide both sides by 5 1 (28 x 24) 13 x 3 3 1 3 (28 x 24) 13 x 33 3 28x 24 39x 9 24 11x 9 33 11x 33 x 11 3 x 5 x 7 33 8 5 8 x 7 338 8 5x 56 264 5x 320 x 64 multiply both sides by 3 to get rid of the fraction distribute the 3 on both sides subtract 9x on both sides subtract 9 on both sides divide both sides by 11 simplified the fraction multiply both sides by 8 to get rid of fraction distribute 8 add 56 to both sides divide by 5 on both sides 4. 4x 7 2x 5x 3 8x 2x 7 3x 3 5x 7 3 5x 10 x 2 combine like terms on both sides add 3x to both sides subtract 7 on both sides divide by 5 on both sides 5. 3x 2(1 x) x 2 3x 2 2x x 2 x2 x2 2 2 No Solution distribute the 2 into each term in the parenthesis combine like terms (3x – 2x) subtract x on both sides the numbers are not equal, so there is no solution for x 6. 5x 2 4 x 4 3 2 5 x 2 4x 4 6 6 3 2 2(5 x 2) (4 x 4)3 10x 4 12x 12 4 2x 12 16 2x 8 x 7. 5 x ( x 3) 5 5x x 3 5 4x 3 5 4x 8 x2 8. 2(4 x 7) (2 3x) 9 8x 14 2 3x 9 11x 16 9 11x 25 3 x2 11 multiply both sides by the common denominator 6 simplify with the denominators distribute on both sides subtract 10x on both sides subtract 12 on both sides divide both sides by 2 distribute the negative into the parenthesis combine like terms (5x – x) add 3 to both sides divide both sides by 4 distribute the 2 and the negative combine like terms (8x + 3x) and (-14 – 2) add 16 to both sides divide both sides by 11 9. 52( x 3) ( x 2) 5x 20 52x 6 x 2 5x 20 5( x 4) 5 x 20 5x 20 5x 20 20 20 Identity 10. 5x 23(1 x) 2(1 x) 22 5x 23 3x 2 2x 22 5 x 2(5 x 1) 22 5x 10x 2 22 5x 2 22 5x 20 x 4 distribute the 2 and the negative in the brackets combine like terms in brackets and change the brackets to parenthesis distribute the 5 in the parenthesis subtract 5x on both sides Whenever to constants are remaining and they are equal, then it is an identity distribute the 3 and the -2 inside the brackets combine like terms in the brackets distribute the 2 into the parenthesis combine like terms (5x – 10x) subtract 2 on both sides divide both sides by -5 11. 2(5 x 4) 3( x 5) 8(2 x 7) 10x 8 3x 15 16x 56 7 x 7 16x 56 7 9x 56 63 9x 7x 12. 13. x 1 3x 6 3 10 5 2 x 1 3x 6 3 10 10 5 2 10 ( x 1) 2(3x 6) (3)5 x 1 6x 12 15 5x 13 15 5x 2 2 x 5 3x 1 4 x 2 3 3 5 5 3x 1 4 x 2 3 15 15 5 5 3 5(3x 1) 3(4 x 2) (3)3 15x 5 12x 6 9 3x 1 9 3x 10 1 x3 3 distribute the 2, -3, and 8 into the parenthesis combine like terms (10x – 3x) and (-8 + 15) subtract 7x on both sides add 56 to both sides divide by 9 on both sides multiply both sides by 10 to get rid of fractions distribute the 10 and simplify distribute the -2 in the parenthesis Combine like terms (x – 6x) and (1 – 12) add 11 to both sides divide both sides by -13 Multiply both sides by the common denominator Simplify denominators and 15 Distribute the 5 and -3 Combine like terms (15x – 12x) and (3 – 6) Add 3 to both sides Divide by 3 on both sides 14. 23( x 2) ( x) 5( x 3) 2(1 x) 23x 6 x 5x 15 2 2x Distributed the 3, negative, 5, and -2 2(4 x 6) 7 x 13 Combine like terms Distributed the 2 into the parenthesis 8x 12 7 x 13 Subtracted 7x on both sides x 12 13 Subtract 12 on both sides x 1 15. The sum of three consecutive odd integers is 81. Find the integers! (n) + (n+2) + (n+4) = 81 3n + 6 = 81 3n = 75 n = 25 So, 25, 27, and 29 are the three consecutive integers that add up to 81!!! 16. One train leaves the station at noon traveling 60 mph. At 2:00 pm a second train leaves the station on a parallel track traveling 90 mph. How long will it take the faster train to overtake the slower one? Rate 60 mph 90 mph Slower Train Faster Train 60t = 90(t – 2) 60t = 90t – 180 -30t = -180 t = 6 hours Time t t–2 Distance 60t 90(t – 2) (This is the time for SLOWER train!!) t–2 =6–2 = 4 hours for the faster train to catch up to the slower train!) 17. The length of a rectangle is 5 more than twice the width. The perimeter is 46. Find the length and width of the rectangle. L = 5 + 2W P = 2L + 2W 46 = 2(5 + 2W) + 2W 46 = 10 + 4W + 2W 46 = 10 + 6W 36 = 6W 6=W L = 5 + 2W L = 5 + 2(6) L = 5 + 12 L = 17