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Simplifying 10(3x + 10) + -5(3x + -2) = 6(6x + 1) + -10(3x + -11) Reorder the terms: 10(10 + 3x) + -5(3x + -2) = 6(6x + 1) + -10(3x + -11) (10 * 10 + 3x * 10) + -5(3x + -2) = 6(6x + 1) + -10(3x + -11) (100 + 30x) + -5(3x + -2) = 6(6x + 1) + -10(3x + -11) Reorder the terms: 100 + 30x + -5(-2 + 3x) = 6(6x + 1) + -10(3x + -11) 100 + 30x + (-2 * -5 + 3x * -5) = 6(6x + 1) + -10(3x + -11) 100 + 30x + (10 + -15x) = 6(6x + 1) + -10(3x + -11) Reorder the terms: 100 + 10 + 30x + -15x = 6(6x + 1) + -10(3x + -11) Combine like terms: 100 + 10 = 110 110 + 30x + -15x = 6(6x + 1) + -10(3x + -11) Combine like terms: 30x + -15x = 15x 110 + 15x = 6(6x + 1) + -10(3x + -11) Reorder the terms: 110 + 15x = 6(1 + 6x) + -10(3x + -11) 110 + 15x = (1 * 6 + 6x * 6) + -10(3x + -11) 110 + 15x = (6 + 36x) + -10(3x + -11) Reorder the terms: 110 + 15x = 6 + 36x + -10(-11 + 3x) 110 + 15x = 6 + 36x + (-11 * -10 + 3x * -10) 110 + 15x = 6 + 36x + (110 + -30x) Reorder the terms: 110 + 15x = 6 + 110 + 36x + -30x Combine like terms: 6 + 110 = 116 110 + 15x = 116 + 36x + -30x Combine like terms: 36x + -30x = 6x 110 + 15x = 116 + 6x Solving 110 + 15x = 116 + 6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6x' to each side of the equation. 110 + 15x + -6x = 116 + 6x + -6x Combine like terms: 15x + -6x = 9x 110 + 9x = 116 + 6x + -6x Combine like terms: 6x + -6x = 0 110 + 9x = 116 + 0 110 + 9x = 116 Add '-110' to each side of the equation. 110 + -110 + 9x = 116 + -110 Combine like terms: 110 + -110 = 0 0 + 9x = 116 + -110 9x = 116 + -110 Combine like terms: 116 + -110 = 6 9x = 6 Divide each side by '9'. x = 0.6666666667 Simplifying x = 0.6666666667
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