.. (18. Cor. 1.) 21x 39 = 10x + 5; .. (17) by transposition, 21 x - 10x = 39 + 5, 24. Given 12 - x ::: 4 : 1, to find the value of x. 2 (21) Since the product of the extremes is equal to the product of the means, .. (17) by transposition, 12 = 2x + x = 3x, :: 7:4, to find the value of x. .. (18. Cor. 2.) 40x + 32 = 126-7x; .. (17) by transposition, 40x + 7x = 126 32, 26. Given (4x + 16) = 12, to find the value of x. (19) squaring both sides of the equation, 4x + 16 = 144; .. (17) by transposition, 4x = 144 - 16 = 128; .. (18. Cor. 2.) x = 32. 128 4 27. Given (2x + 3) + 4 = 7, to find the value of x. (17) by transposition, ☑ (2x + 3) = 7 - 4 = 3; ... (19) cubing both sides of the equation, 2x + 3 = 27; .. (17) by transposition, 2x = 27 - 3 = 24, 28. Given (12 + x) = 2 + ✓ x, to find the value of x. (19) squaring both sides of the equation, 12 + x 4+4 x + x; .. (17. Cor. 3.) 8 = 4√x; and (18. Cor. 2.) 2 = √x; x, to find the value .. (18. Cor. 1.) 21x - 39 = 10x + 5; .. (17) by transposition, 21 - 10x = 39 + 5, 50 12 13, .. (17. Cor. 3.) 366 6. :: 4 : 1, to find the value of x. (21) Since the product of the extremes is equal to the product of the means, .. (17) by transposition, 12 = 2x + x = 3x, :: 7: 4, to find the value of x. .. (18. Cor. 2.) 40x + 32 = 126 - 7x; .. (17) by transposition, 40x + 7x = 126 - 32, or 47 x = 94; 94 ..x = = 2. 47 26. Given (4x + 16) = 12, to find the value of x. (19) squaring both sides of the equation, 4x + 16 = 144 ; .. (17) by transposition, 4x = 144 - 16 = 128; 27. Given (2x + 3) + 4 = 7, to find the value of x. (17) by transposition, ☑ (2x + 3) = 7 - 4 = 3; ... (19) cubing both sides of the equation, 2x + 3 = 27; .. (17) by transposition, 2x = 27 3 = 24, (x + 40) = 10 ✓ x, to find the value 29. Given (19) squaring both sides of the equation, x 16 = 64 16√x + x; .. (17. Cor. 3.) 16 ✓ x = 64 + 16 = 80; 31. Given .. (18. Cor. 2.) ✓ = 5, and (19) x = 25. (x-24) = √x - 2, to find the value of x. (19) squaring both sides of the equation, (19) squaring both sides of the equation, 33. Given x (x + 2) = (19) squaring both sides of the equation, 5x + 2. 4 |