xercises CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. 1. A(n) – is a statement that two expressions are equal. 2. To an equation means to find all numbers that make the equation a true statement. 3. A linear equation is a(n) because the greatest degree of the variable is 1. 4. A(n) is an equation satisfied by every number that is a meaningful replace- ment for the variable. 5. A(n). is an equation that has no solution. CONCEPT PREVIEW Decide whether each statement is true or false. 6. The solution set of 2x + 5 = x – 3 is {-8}. 7. The equation 5(x – 8) = 5x – 40 is an example of an identity. 8. The equation 5x 4x is an example of a contradiction. 9. Solving the literal equation A = ; bh for the variable h gives h 2b• 10. CONCEPT PREVIE W Which one is not a linear equation? A. 5x + 7(x – 1) = -3x B. 9x2 - 4x + 3 = 0 C. 7x + 8x = 13x D. 0.04x - 0.08x = 0.40 %3D %3D Solve each equation. See Examples 1 and 2. 11. 5x + 4 = 3x - 4 12. 9x + 11 = 7x + 1 %3D (13, 6(3x – 1) = 8 – (10x – 14) 14. 4(-2x + 1) = 6 – (2x – 4) %3D 5 15. -x 4 5 4 - 2x+ 16. X + -x 5* 2 5* 3 3 4. 17. 3x + 5 – 5(x + 1) = 6x + 7 18. 5(x + 3) + 4.x - 3 = -(2x - 4)+ 2 19. 2[x - (4 + 2x) + 3] = 2x + 2 20. 4[2x – (3 - x) + 5] = -6x – 28 %3D x + 10 x + 2 (3x – (21(3x-2) = - (3х — 2) : (2x+5) 22. %3D 10 15 24. 0.01x + 3.1 = 2.03x - 2.96 23. 0.2x- 0.5 = 0.1x + 7 25. -4(2x- 6) + 8x = 5x + 24 + x 26. -8(3x + 4) + 6x = 4(x - 8) + 4x 4 27. 0.5x + x= x+ 10 3 28. x+ +.25x x+ 2 3 29. 0.08x + 0.06(x+ 12)= 7.72 30. 0.04(x - 12) + 0.06.x = 1.52 %3D Determine whether each equation is an identity, a conditional equation, or a contradic- tion. Give the solution set. See Example 3. 1 31. 4(2x + 7) = 2x + 22 + 3(2x + 2) 32. (6x + 20) = x + 4 + 2(x+ 3) (33) 2(x- 8) = 3x - 16 34. -8(x+ 5)= -8x – 5(x+ 8) %3D 35, 4(x+ 7) = 2(x + 12) + 2(x + 1) 36. –6(2x + 1) – 3(x – 4) = -15x + 1 %3D 37. 0.3(x + 2) – 0.5(x + 2) = -0.2x – 0.4 38. -0.6(x – 5) + 0.8(x – 6) = 0.2x – 1.8 Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. See Examples 4(a) and (b). 39 V= lwh, (volume of a rectangular box) for l 40. I = Prt, (simple interest) for P 41. P = a + b + c, (perimeter of a triangle) for c 42. P = 21 + 2w, for w (perimeter of a rectangle) h(B + b), 43. A = (area of a trapezoid) for B h(B+ b), (area of a trapezoid) for h %3D 45. S= 2rrh + 2™r², (surface area of a right circular cylinder) for h 46. . 8t2, (distance traveled by a falling object) for g 281 47 S= 2lw + 2wh + 2hl, for h (surface area of a rectangular box) anillaboM b ns anoitilqgA SI anoitsup llqbA (standardized value) 48. z = for x Solve each equation for x. See Example 4(c). dong 50. 5x- (2a + c) = 4(x + c) 49, 2(x- a) + b = 3x + a lot od amoldog %3D 52. 4а - ах %3 3Ь + bx 31. ax + b = 3(x – a) x-1 = 2x- a 2a 54. - = ax + 3 53. 56. ax + b? = bx - a? 55. a'x + 3x = 2a? %3D %3D 58. -x = (5x + 3)(3k + 1) 57. 3x (2x- 1)(m + 4) Work each problem. See Example 5. Simple Interest 59. Elmer borowed $3150 from his brother Julio to pay for books and tuition. He agreed to repay Julio in 6 months with simple annual interest at 4%. (a) How much will the interest amount to? (b) What amount must Elmer pay Julio at the end of the 6 months? 60. Levada borrows $30,900 from her bank to open a florist shop. She agrees to repay money in 18 months with simple annual interest of 5.5%. th (a) How much must she pay the bank in 18 months? (hì How much of the amount in part (a) is interest?
xercises CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. 1. A(n) – is a statement that two expressions are equal. 2. To an equation means to find all numbers that make the equation a true statement. 3. A linear equation is a(n) because the greatest degree of the variable is 1. 4. A(n) is an equation satisfied by every number that is a meaningful replace- ment for the variable. 5. A(n). is an equation that has no solution. CONCEPT PREVIEW Decide whether each statement is true or false. 6. The solution set of 2x + 5 = x – 3 is {-8}. 7. The equation 5(x – 8) = 5x – 40 is an example of an identity. 8. The equation 5x 4x is an example of a contradiction. 9. Solving the literal equation A = ; bh for the variable h gives h 2b• 10. CONCEPT PREVIE W Which one is not a linear equation? A. 5x + 7(x – 1) = -3x B. 9x2 - 4x + 3 = 0 C. 7x + 8x = 13x D. 0.04x - 0.08x = 0.40 %3D %3D Solve each equation. See Examples 1 and 2. 11. 5x + 4 = 3x - 4 12. 9x + 11 = 7x + 1 %3D (13, 6(3x – 1) = 8 – (10x – 14) 14. 4(-2x + 1) = 6 – (2x – 4) %3D 5 15. -x 4 5 4 - 2x+ 16. X + -x 5* 2 5* 3 3 4. 17. 3x + 5 – 5(x + 1) = 6x + 7 18. 5(x + 3) + 4.x - 3 = -(2x - 4)+ 2 19. 2[x - (4 + 2x) + 3] = 2x + 2 20. 4[2x – (3 - x) + 5] = -6x – 28 %3D x + 10 x + 2 (3x – (21(3x-2) = - (3х — 2) : (2x+5) 22. %3D 10 15 24. 0.01x + 3.1 = 2.03x - 2.96 23. 0.2x- 0.5 = 0.1x + 7 25. -4(2x- 6) + 8x = 5x + 24 + x 26. -8(3x + 4) + 6x = 4(x - 8) + 4x 4 27. 0.5x + x= x+ 10 3 28. x+ +.25x x+ 2 3 29. 0.08x + 0.06(x+ 12)= 7.72 30. 0.04(x - 12) + 0.06.x = 1.52 %3D Determine whether each equation is an identity, a conditional equation, or a contradic- tion. Give the solution set. See Example 3. 1 31. 4(2x + 7) = 2x + 22 + 3(2x + 2) 32. (6x + 20) = x + 4 + 2(x+ 3) (33) 2(x- 8) = 3x - 16 34. -8(x+ 5)= -8x – 5(x+ 8) %3D 35, 4(x+ 7) = 2(x + 12) + 2(x + 1) 36. –6(2x + 1) – 3(x – 4) = -15x + 1 %3D 37. 0.3(x + 2) – 0.5(x + 2) = -0.2x – 0.4 38. -0.6(x – 5) + 0.8(x – 6) = 0.2x – 1.8 Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. See Examples 4(a) and (b). 39 V= lwh, (volume of a rectangular box) for l 40. I = Prt, (simple interest) for P 41. P = a + b + c, (perimeter of a triangle) for c 42. P = 21 + 2w, for w (perimeter of a rectangle) h(B + b), 43. A = (area of a trapezoid) for B h(B+ b), (area of a trapezoid) for h %3D 45. S= 2rrh + 2™r², (surface area of a right circular cylinder) for h 46. . 8t2, (distance traveled by a falling object) for g 281 47 S= 2lw + 2wh + 2hl, for h (surface area of a rectangular box) anillaboM b ns anoitilqgA SI anoitsup llqbA (standardized value) 48. z = for x Solve each equation for x. See Example 4(c). dong 50. 5x- (2a + c) = 4(x + c) 49, 2(x- a) + b = 3x + a lot od amoldog %3D 52. 4а - ах %3 3Ь + bx 31. ax + b = 3(x – a) x-1 = 2x- a 2a 54. - = ax + 3 53. 56. ax + b? = bx - a? 55. a'x + 3x = 2a? %3D %3D 58. -x = (5x + 3)(3k + 1) 57. 3x (2x- 1)(m + 4) Work each problem. See Example 5. Simple Interest 59. Elmer borowed $3150 from his brother Julio to pay for books and tuition. He agreed to repay Julio in 6 months with simple annual interest at 4%. (a) How much will the interest amount to? (b) What amount must Elmer pay Julio at the end of the 6 months? 60. Levada borrows $30,900 from her bank to open a florist shop. She agrees to repay money in 18 months with simple annual interest of 5.5%. th (a) How much must she pay the bank in 18 months? (hì How much of the amount in part (a) is interest?
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter1: Introduction To Algebra
Section1.4: Translating Words Into Symbols
Problem 54WE
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