Algebra Fundamentals of Algebra Order of Precedence: 1. Parenthesis 2. Exponentials (squares, square roots, etc.) 3. Multiplication and Division 4. Addition and Subtraction Examples I: Use a = 15, b = 3, t = 4, solve each equation for "x" 1. x = (a – b) / t Solution: x = (15 – 3) / 4 x = 12 / 4 x = 3 2. x = (2(a – b) + 3b – 5) / (t + b) Solution: x = 2 · (15 – 3) + 3(3) – 5 / (4 + 3) x = 2 · (12) + 9 – 5 / 7 x = 4 3. x = 2(a – b)2 / 10 Solution: x = 2 · (15 – 3)2 / 10 x = 2 · (12)2 / 10 x = 2 · (144) / 10 x = 28.8 Examples II: Use the following formula to compute the desired quantity: d = v t + ½ a t2 1. If v = 5, t = 2, a = 10; what is d ? Solution: d = 5(2) + ½ · (10) · (2)2 d = 10 + ½ · (10) · (4) d = 30 2. If d = 80, t = 2, a = 10; what is v ? Solution: d = v · t + ½ a t2 v · t = d – ½ a t2 v = (d – ½ a t2) / t v = 80 – ½(10)(22) / 2 v = (80 – 20) / 2 v = 60 / 20 v = 3More Practice Algebra Problems Solve for x unless otherwise instructed: 1) 3x = 17 2) x/5 = 13 3) x/3 + 21 = 14 4) 2(5-x) = 10(20x – 7) 5) (15/x + 3)7 – 9x = 0 6) 5x2 = 17 7) 1/4x2 – 3/5 = 5/7 8) 3x / 8 – 1/3 = 15 9) d = ½(at2) Solve for t in terms of a and d 10) Vf2 = Vi2 + 2ad Solve for d in terms of Vi, Vf, and aPractice Algebra Problems Solutions 1) x = 17/3 x = 5.67 2) x = 13(5) x = 65 3) x/3 + 21 = 14 x/3 = 14 – 21 x/3 = –7 x = –7(3) x = –21 4) 2(5–x) = 10(20x – 7) 10 – 2x = 200x – 70 200x + 2x = 10 + 70 202x = 80 x = 80/202 x = 0.396 5) (15/x + 3)7 – 9x = 0 105/x + 21 = 9x 105 + 21x = 9x2 9x2 –21x – 105 = 0 (use the quadratic equation) xbb4ac2ax21 21 4(9)( 105)2(9)x21 441 378018x21 422118x21 64.9718x21 64.9718x = 4.776 or - .22=−± −=±− − −=±+=±=±=±2443 6) 5x2 = 17 x2 = 17/5 x = 17 5/ x = 1.84 7) 1/4x2 – 3/5 = 5/7 1/4x2 = 5/7 + 3/5 1/4x2 = 25/35 + 21/35 x2 = 46/35 * 4 x2 = 5.257 x = 5257. x = 2.29 8) 3x / 8 – 1/3 = 15 3x / 8 = 15 + 1/3 3x = 8 (15 + 1/3) 3x = 8 (15.33) 3x = 122.64 x = 122.64 / 3 x = 40.88 9) d = 1/2at2 (Solve for t in terms of a and d) t2 = 2d / a t2da= 10) Vf2 = Vi2+ 2ad (Solve for d in terms of Vf and a)