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Simplifying k(k + 1)(k + 2)(k + 3) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) Reorder the terms: k(1 + k)(k + 2)(k + 3) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) Reorder the terms: k(1 + k)(2 + k)(k + 3) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) Reorder the terms: k(1 + k)(2 + k)(3 + k) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) Multiply (1 + k) * (2 + k) k(1(2 + k) + k(2 + k))(3 + k) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) k((2 * 1 + k * 1) + k(2 + k))(3 + k) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) k((2 + 1k) + k(2 + k))(3 + k) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) k(2 + 1k + (2 * k + k * k))(3 + k) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) k(2 + 1k + (2k + k2))(3 + k) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) Combine like terms: 1k + 2k = 3k k(2 + 3k + k2)(3 + k) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) Multiply (2 + 3k + k2) * (3 + k) k(2(3 + k) + 3k * (3 + k) + k2(3 + k)) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) k((3 * 2 + k * 2) + 3k * (3 + k) + k2(3 + k)) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) k((6 + 2k) + 3k * (3 + k) + k2(3 + k)) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) k(6 + 2k + (3 * 3k + k * 3k) + k2(3 + k)) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) k(6 + 2k + (9k + 3k2) + k2(3 + k)) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) k(6 + 2k + 9k + 3k2 + (3 * k2 + k * k2)) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) k(6 + 2k + 9k + 3k2 + (3k2 + k3)) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) Combine like terms: 2k + 9k = 11k k(6 + 11k + 3k2 + 3k2 + k3) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) Combine like terms: 3k2 + 3k2 = 6k2 k(6 + 11k + 6k2 + k3) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) (6 * k + 11k * k + 6k2 * k + k3 * k) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) (6k + 11k2 + 6k3 + k4) + 4k(k + 2)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) Reorder the terms: 6k + 11k2 + 6k3 + k4 + 4k(2 + k)(k + 3) = k + 1(k + 2)(k + 3)(k + 4) Reorder the terms: 6k + 11k2 + 6k3 + k4 + 4k(2 + k)(3 + k) = k + 1(k + 2)(k + 3)(k + 4) Multiply (2 + k) * (3 + k) 6k + 11k2 + 6k3 + k4 + 4k(2(3 + k) + k(3 + k)) = k + 1(k + 2)(k + 3)(k + 4) 6k + 11k2 + 6k3 + k4 + 4k((3 * 2 + k * 2) + k(3 + k)) = k + 1(k + 2)(k + 3)(k + 4) 6k + 11k2 + 6k3 + k4 + 4k((6 + 2k) + k(3 + k)) = k + 1(k + 2)(k + 3)(k + 4) 6k + 11k2 + 6k3 + k4 + 4k(6 + 2k + (3 * k + k * k)) = k + 1(k + 2)(k + 3)(k + 4) 6k + 11k2 + 6k3 + k4 + 4k(6 + 2k + (3k + k2)) = k + 1(k + 2)(k + 3)(k + 4) Combine like terms: 2k + 3k = 5k 6k + 11k2 + 6k3 + k4 + 4k(6 + 5k + k2) = k + 1(k + 2)(k + 3)(k + 4) 6k + 11k2 + 6k3 + k4 + (6 * 4k + 5k * 4k + k2 * 4k) = k + 1(k + 2)(k + 3)(k + 4) 6k + 11k2 + 6k3 + k4 + (24k + 20k2 + 4k3) = k + 1(k + 2)(k + 3)(k + 4) Reorder the terms: 6k + 24k + 11k2 + 20k2 + 6k3 + 4k3 + k4 = k + 1(k + 2)(k + 3)(k + 4) Combine like terms: 6k + 24k = 30k 30k + 11k2 + 20k2 + 6k3 + 4k3 + k4 = k + 1(k + 2)(k + 3)(k + 4) Combine like terms: 11k2 + 20k2 = 31k2 30k + 31k2 + 6k3 + 4k3 + k4 = k + 1(k + 2)(k + 3)(k + 4) Combine like terms: 6k3 + 4k3 = 10k3 30k + 31k2 + 10k3 + k4 = k + 1(k + 2)(k + 3)(k + 4) Reorder the terms: 30k + 31k2 + 10k3 + k4 = k + 1(2 + k)(k + 3)(k + 4) Reorder the terms: 30k + 31k2 + 10k3 + k4 = k + 1(2 + k)(3 + k)(k + 4) Reorder the terms: 30k + 31k2 + 10k3 + k4 = k + 1(2 + k)(3 + k)(4 + k) Multiply (2 + k) * (3 + k) 30k + 31k2 + 10k3 + k4 = k + 1(2(3 + k) + k(3 + k))(4 + k) 30k + 31k2 + 10k3 + k4 = k + 1((3 * 2 + k * 2) + k(3 + k))(4 + k) 30k + 31k2 + 10k3 + k4 = k + 1((6 + 2k) + k(3 + k))(4 + k) 30k + 31k2 + 10k3 + k4 = k + 1(6 + 2k + (3 * k + k * k))(4 + k) 30k + 31k2 + 10k3 + k4 = k + 1(6 + 2k + (3k + k2))(4 + k) Combine like terms: 2k + 3k = 5k 30k + 31k2 + 10k3 + k4 = k + 1(6 + 5k + k2)(4 + k) Multiply (6 + 5k + k2) * (4 + k) 30k + 31k2 + 10k3 + k4 = k + 1(6(4 + k) + 5k * (4 + k) + k2(4 + k)) 30k + 31k2 + 10k3 + k4 = k + 1((4 * 6 + k * 6) + 5k * (4 + k) + k2(4 + k)) 30k + 31k2 + 10k3 + k4 = k + 1((24 + 6k) + 5k * (4 + k) + k2(4 + k)) 30k + 31k2 + 10k3 + k4 = k + 1(24 + 6k + (4 * 5k + k * 5k) + k2(4 + k)) 30k + 31k2 + 10k3 + k4 = k + 1(24 + 6k + (20k + 5k2) + k2(4 + k)) 30k + 31k2 + 10k3 + k4 = k + 1(24 + 6k + 20k + 5k2 + (4 * k2 + k * k2)) 30k + 31k2 + 10k3 + k4 = k + 1(24 + 6k + 20k + 5k2 + (4k2 + k3)) Combine like terms: 6k + 20k = 26k 30k + 31k2 + 10k3 + k4 = k + 1(24 + 26k + 5k2 + 4k2 + k3) Combine like terms: 5k2 + 4k2 = 9k2 30k + 31k2 + 10k3 + k4 = k + 1(24 + 26k + 9k2 + k3) 30k + 31k2 + 10k3 + k4 = k + (24 * 1 + 26k * 1 + 9k2 * 1 + k3 * 1) 30k + 31k2 + 10k3 + k4 = k + (24 + 26k + 9k2 + 1k3) Reorder the terms: 30k + 31k2 + 10k3 + k4 = 24 + k + 26k + 9k2 + 1k3 Combine like terms: k + 26k = 27k 30k + 31k2 + 10k3 + k4 = 24 + 27k + 9k2 + 1k3 Solving 30k + 31k2 + 10k3 + k4 = 24 + 27k + 9k2 + 1k3 Solving for variable 'k'. Reorder the terms: -24 + 30k + -27k + 31k2 + -9k2 + 10k3 + -1k3 + k4 = 24 + 27k + 9k2 + 1k3 + -24 + -27k + -9k2 + -1k3 Combine like terms: 30k + -27k = 3k -24 + 3k + 31k2 + -9k2 + 10k3 + -1k3 + k4 = 24 + 27k + 9k2 + 1k3 + -24 + -27k + -9k2 + -1k3 Combine like terms: 31k2 + -9k2 = 22k2 -24 + 3k + 22k2 + 10k3 + -1k3 + k4 = 24 + 27k + 9k2 + 1k3 + -24 + -27k + -9k2 + -1k3 Combine like terms: 10k3 + -1k3 = 9k3 -24 + 3k + 22k2 + 9k3 + k4 = 24 + 27k + 9k2 + 1k3 + -24 + -27k + -9k2 + -1k3 Reorder the terms: -24 + 3k + 22k2 + 9k3 + k4 = 24 + -24 + 27k + -27k + 9k2 + -9k2 + 1k3 + -1k3 Combine like terms: 24 + -24 = 0 -24 + 3k + 22k2 + 9k3 + k4 = 0 + 27k + -27k + 9k2 + -9k2 + 1k3 + -1k3 -24 + 3k + 22k2 + 9k3 + k4 = 27k + -27k + 9k2 + -9k2 + 1k3 + -1k3 Combine like terms: 27k + -27k = 0 -24 + 3k + 22k2 + 9k3 + k4 = 0 + 9k2 + -9k2 + 1k3 + -1k3 -24 + 3k + 22k2 + 9k3 + k4 = 9k2 + -9k2 + 1k3 + -1k3 Combine like terms: 9k2 + -9k2 = 0 -24 + 3k + 22k2 + 9k3 + k4 = 0 + 1k3 + -1k3 -24 + 3k + 22k2 + 9k3 + k4 = 1k3 + -1k3 Combine like terms: 1k3 + -1k3 = 0 -24 + 3k + 22k2 + 9k3 + k4 = 0 The solution to this equation could not be determined.
| 3.5y=y+6.3 | | 3x-0.6x=14 | | 4(n+6)-(n-6)= | | -1.27-4.6b=7.93 | | 48=11y+26 | | -10-2y=5x+32 | | ln(x^2-5)=ln(4x) | | 2A+3A=24 | | 4-(-0.3)=8 | | 5=2/3x+7 | | 10(p+5)-8(p-3)= | | -3+(y/4)=1 | | 12(w+.67)=10.2 | | 7x-(3x+5)+9=2x | | -x+4-x+6x=4 | | 8b+11-3h=2h+2 | | 3(X-2)+10=5x | | 21y-24=12 | | 2x^2-5x+7+5x^2-3+x^2-x+11= | | 9y+1=80 | | 9(x+0.14)=18 | | 5x^3-25x^2+20x= | | 2y+3y+10= | | 25x^4+8x=O | | 10(5r-4)+3(8r+6)= | | 2x+10+3x=-12x+70 | | 5x+(-25)=-65 | | 14(4-x)=12(2-x) | | 4(c-n)=100 | | 6x+5(2x-14)=58 | | 12h-(6h-5)+18= | | x^2+18x+81=6-x |