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Simplifying 9e + -6[(3e + 4) + -1(5e + -7)] = 18 + -4[3(2e + -5) + -1d] Reorder the terms: 9e + -6[(4 + 3e) + -1(5e + -7)] = 18 + -4[3(2e + -5) + -1d] Remove parenthesis around (4 + 3e) 9e + -6[4 + 3e + -1(5e + -7)] = 18 + -4[3(2e + -5) + -1d] Reorder the terms: 9e + -6[4 + 3e + -1(-7 + 5e)] = 18 + -4[3(2e + -5) + -1d] 9e + -6[4 + 3e + (-7 * -1 + 5e * -1)] = 18 + -4[3(2e + -5) + -1d] 9e + -6[4 + 3e + (7 + -5e)] = 18 + -4[3(2e + -5) + -1d] Reorder the terms: 9e + -6[4 + 7 + 3e + -5e] = 18 + -4[3(2e + -5) + -1d] Combine like terms: 4 + 7 = 11 9e + -6[11 + 3e + -5e] = 18 + -4[3(2e + -5) + -1d] Combine like terms: 3e + -5e = -2e 9e + -6[11 + -2e] = 18 + -4[3(2e + -5) + -1d] 9e + [11 * -6 + -2e * -6] = 18 + -4[3(2e + -5) + -1d] 9e + [-66 + 12e] = 18 + -4[3(2e + -5) + -1d] Reorder the terms: -66 + 9e + 12e = 18 + -4[3(2e + -5) + -1d] Combine like terms: 9e + 12e = 21e -66 + 21e = 18 + -4[3(2e + -5) + -1d] Reorder the terms: -66 + 21e = 18 + -4[3(-5 + 2e) + -1d] -66 + 21e = 18 + -4[(-5 * 3 + 2e * 3) + -1d] -66 + 21e = 18 + -4[(-15 + 6e) + -1d] Reorder the terms: -66 + 21e = 18 + -4[-15 + -1d + 6e] -66 + 21e = 18 + [-15 * -4 + -1d * -4 + 6e * -4] -66 + 21e = 18 + [60 + 4d + -24e] Combine like terms: 18 + 60 = 78 -66 + 21e = 78 + 4d + -24e Solving -66 + 21e = 78 + 4d + -24e Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Add '24e' to each side of the equation. -66 + 21e + 24e = 78 + 4d + -24e + 24e Combine like terms: 21e + 24e = 45e -66 + 45e = 78 + 4d + -24e + 24e Combine like terms: -24e + 24e = 0 -66 + 45e = 78 + 4d + 0 -66 + 45e = 78 + 4d Add '66' to each side of the equation. -66 + 66 + 45e = 78 + 66 + 4d Combine like terms: -66 + 66 = 0 0 + 45e = 78 + 66 + 4d 45e = 78 + 66 + 4d Combine like terms: 78 + 66 = 144 45e = 144 + 4d Divide each side by '45'. e = 3.2 + 0.08888888889d Simplifying e = 3.2 + 0.08888888889d
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