1) Simplify the expression: 2) Solve the equation: 3) Solve the equation: 4) Solve the equation: 5) Solve the equation: 6) Solve the inequality. Write your answer in interval notation and graph the solution set on a number line: 7) Solve the inequality. Write your answer in interval notation and graph the solution set on a number line: 8) Solve the inequality. Write your answer in interval notation and graph the solution set on a number line: 9) Solve the inequality. Write your answer in interval notation and graph the solution set on a number line: 10) Amber paid $27,375 as a down payment for her house. If the down payment was 15% of the actual cost of the house, what was the actual cost? 11) After Sarah received a 5% raise, her annual salary was $71,400. What was her annual salary before the raise? 12) Marcus wins $800,000 (after taxes) in the lottery and decides to invest half of it in a 5-year CD that pays 5.24% interest compounded quarterly. He invests the other half in a money market fund that unfortunately turns out to average only 1.8% interest compounded annually over the 5-year period. How much money will he have altogether in the two accounts at the end of the 5-year period? 13) Line a has a slope of 6. If line b is perpendicular to line a, what is the slope of line b? 14) Given the points (5, -3) and (-7, 1): a) Find the slope of the line through the points. b) Write an equation in point-slope form of the line through the points. c) Convert the equation to slope-intercept form. d) Convert the equation to standard form. e) Graph the equation. You may use the axes provided, or create your own graph. 15) a) Write an equation of a vertical line through the point (-3, 5). b) Write an equation of a horizontal line through the point (-7, -2). c) Find the slope of a line parallel to the line with equation 3x - 7y = 21. d) Find the slope of a line perpendicular to the line with equation 2x + 3y = 5. 1. Simplify the expression: (-4^2-2(5^2-3^2))/(6-|2-12|) solving the powers 162 ( 259 ) 6|212| Solving the bracketsabsolute valu e 162 ( 16 ) 6|10| 1632 610 16 4 4 2. Solve the equation: 6(x-4)=9(2-x) Expanding the brackets 6x64=929x 6 x24=189 x Adding 9 x on both sides of the equation 6 x24+ 9 x=189 x +9 x 15 x24=18 Adding 24 both sides of the equation 15 x24+24=18+ 24 15 x=42 x= 42 15 x=2.8 3. Solve the equation: 3(5x+1)=4(6x-1)-3(3x-2) Expanding the brackets 15 x+3=24 x49 x+ 6 Collectinglike termssolving 15 x+ 9 x24 x=4+ 63 24 x24 x=7+ 6 0 x=1 Has no solution 4. Solve the equation: (3x+4)/5-(2x-1)/3=3 Multiplying both sides by 15( L .C . M of 53) 15 =3 15 ( 3 x+5 4 2 x1 3 ) 3(3 x +4)5(2 x1)=45 Expanding the brackets 9 x+ 1210 x+5=45 Collectinglike terms 9 x10 x+12+5=45 x=4517 x 28 = 1 1 Dividing the equation by 1 x=28 5. Solve the equation: 0.8x-44=0.5x-1.5 Collecting like terms 0.8 x0.5 x=1.4+ 4.4 0.3 x=3 x= 3 0.3 x=10 6. 4x-9>9x+1 Subtracting 9 x on both sides of the equation 4 x 99 x >9 x +19 x 5 x9>1 Adding 9 on bothsides of the equation 5 x9+9>1+9 5 x >10 Dividing all thoughby5 (sign changes) 5 x 10 > 5 5 x<2 interval notation (,2) Number line 7. 3x/5-10/3<=-5x/3+6/5 Multiplyingby 15(L .C . M of 3,5) ( 35x 103 )( 53 x + 65 )15 3x 10 5 x 6 3 ( )5 ( )5 ( +3 ( ) ) 5 3 3 5 15 9 x5025 x +18 Adding 25 x both sides of the equation 9 x50+25 x25 x+18+ 25 x 34 x5018 Adding 50 both sides of the equation 34 x50+5018+50 34 x68 x 68 34 x2 Interval notation Number line 8. 5<=4x-3<15 Adding 3 the whole equation 5+34 x3+ 3<15+3 84 x <18 Dividing all through by 4 8 4 x 18 < 4 4 4 2x <4.5 Interval notation Number line 9. -14<7-3x<=22 Subtracting 7 both sides of the equation 147< 773 x227 21<3 x15 Dividing all through by3 21 3 x 15 < 3 3 3 7> x5 5x <7 interval notation number line 10. down payment = $ 27,375 15 100 27375 $ 182500 11. after 5% raise, salary =$ 71 400 105 71400 68000 12. total amount 800,000 investment in cd time =5 years principal =400,000 interest =5.24% compounded quarterly r a 1+ n t ( ) 0.0524 400,000 4 5 1+0.0131 1.0131 )20 400,000(1.2973) 518927.04 20 money market fund 1.8 % annually 1+r 0.018 1.018 )5 400,000(1.0933) 437319.54 received =$ 437319.54+ 956246.58 13. let slope of be ma b, mb =? for perpendicular lines , mamb =1 1 substituting the values 6 b =1 14. given points (5, -3) and (-7, 1): a. m y (change x 13 75 12 3 b. equation point-slope form through points. point form, xx 1) y3 =y +3 x5 (x5) c. to slope-intercept form. part . multiplying both sides by y+ (13 )) 9 +5 subtracting 99 =x+ 59 dividing gives slopeintercept d. standard ax + c adding1 on x+ e. graph 15. vertical (-3, 5). line, value is constant whilechanges. taking second 51 33 3+3 0 isundefined formula since defined) horizontal -2). (1, -2) 22 17 2+2 8 2 x7 +2 x+7 cross 0(x +7)=( +2) parallel with - 7 21. are equal writingslopeintercept x3 +21 by7 5. m1 1. simplify expression: (-4^2-2(5^2-3^2)) (6-|2-12|) solving powers 162 259 6|212| bracketsabsolute valu e 16 6|10| 1632 610 2. solve equation: 6(x-4) =9(2-x) expanding brackets 6x64 =929x x24 adding x24+ +9 24 x24+24 =18+ 42 3. 3(5x+1) =4(6x-1)-3(3x-2) x+3 =24 x49 collectinglike termssolving 63 has no solution 4. (3x+4) 5-(2x-1) 15( l .c 53) x+5 x1 3(3 +4)5(2 x1) =45 1210 terms x10 x+12+5 =45 28 =1 0.8x-44 =0.5x-1.5 collecting like 0.8 x0.5 4.4 0.3 6. 4x-9>9x+1 Subtracting 9 x on both sides of the equation 4 x 99 x >9 x +19 x 5 x9>1 Adding 9 on bothsides of the equation 5 x9+9>1+9 5 x >10 Dividing all thoughby5 (sign changes) 5 x 10 > 5 5 x<2 interval notation (,2) Number line 7. 3x/5-10/3<=-5x/3+6/5 Multiplyingby 15(L .C . M of 3,5) ( 35x 103 )( 53 x + 65 )15 3x 10 5 x 6 3 ( )5 ( )5 ( +3 ( ) ) 5 3 3 5 15 9 x5025 x +18 Adding 25 x both sides of the equation 9 x50+25 x25 x+18+ 25 x 34 x5018 Adding 50 both sides of the equation 34 x50+5018+50 34 x68 x 68 34 x2 Interval notation Number line 8. 5<=4x-3<15 Adding 3 the whole equation 5+34 x3+ 3<15+3 84 x <18 Dividing all through by 4 8 4 x 18 < 4 4 4 2x <4.5 Interval notation Number line 9. -14<7-3x<=22 Subtracting 7 both sides of the equation 147< 773 x227 21<3 x15 Dividing all through by3 21 3 x 15 < 3 3 3 7> x5 5x <7 line