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Simplifying 3(2(x + -2) + -7(2x + -3)) + -5(4(2j + -5) + -1(3x + -2)) = 6x + 7 Reorder the terms: 3(2(-2 + x) + -7(2x + -3)) + -5(4(2j + -5) + -1(3x + -2)) = 6x + 7 3((-2 * 2 + x * 2) + -7(2x + -3)) + -5(4(2j + -5) + -1(3x + -2)) = 6x + 7 3((-4 + 2x) + -7(2x + -3)) + -5(4(2j + -5) + -1(3x + -2)) = 6x + 7 Reorder the terms: 3(-4 + 2x + -7(-3 + 2x)) + -5(4(2j + -5) + -1(3x + -2)) = 6x + 7 3(-4 + 2x + (-3 * -7 + 2x * -7)) + -5(4(2j + -5) + -1(3x + -2)) = 6x + 7 3(-4 + 2x + (21 + -14x)) + -5(4(2j + -5) + -1(3x + -2)) = 6x + 7 Reorder the terms: 3(-4 + 21 + 2x + -14x) + -5(4(2j + -5) + -1(3x + -2)) = 6x + 7 Combine like terms: -4 + 21 = 17 3(17 + 2x + -14x) + -5(4(2j + -5) + -1(3x + -2)) = 6x + 7 Combine like terms: 2x + -14x = -12x 3(17 + -12x) + -5(4(2j + -5) + -1(3x + -2)) = 6x + 7 (17 * 3 + -12x * 3) + -5(4(2j + -5) + -1(3x + -2)) = 6x + 7 (51 + -36x) + -5(4(2j + -5) + -1(3x + -2)) = 6x + 7 Reorder the terms: 51 + -36x + -5(4(-5 + 2j) + -1(3x + -2)) = 6x + 7 51 + -36x + -5((-5 * 4 + 2j * 4) + -1(3x + -2)) = 6x + 7 51 + -36x + -5((-20 + 8j) + -1(3x + -2)) = 6x + 7 Reorder the terms: 51 + -36x + -5(-20 + 8j + -1(-2 + 3x)) = 6x + 7 51 + -36x + -5(-20 + 8j + (-2 * -1 + 3x * -1)) = 6x + 7 51 + -36x + -5(-20 + 8j + (2 + -3x)) = 6x + 7 Reorder the terms: 51 + -36x + -5(-20 + 2 + 8j + -3x) = 6x + 7 Combine like terms: -20 + 2 = -18 51 + -36x + -5(-18 + 8j + -3x) = 6x + 7 51 + -36x + (-18 * -5 + 8j * -5 + -3x * -5) = 6x + 7 51 + -36x + (90 + -40j + 15x) = 6x + 7 Reorder the terms: 51 + 90 + -40j + -36x + 15x = 6x + 7 Combine like terms: 51 + 90 = 141 141 + -40j + -36x + 15x = 6x + 7 Combine like terms: -36x + 15x = -21x 141 + -40j + -21x = 6x + 7 Reorder the terms: 141 + -40j + -21x = 7 + 6x Solving 141 + -40j + -21x = 7 + 6x Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-141' to each side of the equation. 141 + -40j + -141 + -21x = 7 + -141 + 6x Reorder the terms: 141 + -141 + -40j + -21x = 7 + -141 + 6x Combine like terms: 141 + -141 = 0 0 + -40j + -21x = 7 + -141 + 6x -40j + -21x = 7 + -141 + 6x Combine like terms: 7 + -141 = -134 -40j + -21x = -134 + 6x Add '21x' to each side of the equation. -40j + -21x + 21x = -134 + 6x + 21x Combine like terms: -21x + 21x = 0 -40j + 0 = -134 + 6x + 21x -40j = -134 + 6x + 21x Combine like terms: 6x + 21x = 27x -40j = -134 + 27x Divide each side by '-40'. j = 3.35 + -0.675x Simplifying j = 3.35 + -0.675x
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