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Simplifying 5(2x + 1) + 3(3x + -2) = 7 + 2(3x + -5) Reorder the terms: 5(1 + 2x) + 3(3x + -2) = 7 + 2(3x + -5) (1 * 5 + 2x * 5) + 3(3x + -2) = 7 + 2(3x + -5) (5 + 10x) + 3(3x + -2) = 7 + 2(3x + -5) Reorder the terms: 5 + 10x + 3(-2 + 3x) = 7 + 2(3x + -5) 5 + 10x + (-2 * 3 + 3x * 3) = 7 + 2(3x + -5) 5 + 10x + (-6 + 9x) = 7 + 2(3x + -5) Reorder the terms: 5 + -6 + 10x + 9x = 7 + 2(3x + -5) Combine like terms: 5 + -6 = -1 -1 + 10x + 9x = 7 + 2(3x + -5) Combine like terms: 10x + 9x = 19x -1 + 19x = 7 + 2(3x + -5) Reorder the terms: -1 + 19x = 7 + 2(-5 + 3x) -1 + 19x = 7 + (-5 * 2 + 3x * 2) -1 + 19x = 7 + (-10 + 6x) Combine like terms: 7 + -10 = -3 -1 + 19x = -3 + 6x Solving -1 + 19x = -3 + 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. -1 + 19x + -6x = -3 + 6x + -6x Combine like terms: 19x + -6x = 13x -1 + 13x = -3 + 6x + -6x Combine like terms: 6x + -6x = 0 -1 + 13x = -3 + 0 -1 + 13x = -3 Add '1' to each side of the equation. -1 + 1 + 13x = -3 + 1 Combine like terms: -1 + 1 = 0 0 + 13x = -3 + 1 13x = -3 + 1 Combine like terms: -3 + 1 = -2 13x = -2 Divide each side by '13'. x = -0.1538461538 Simplifying x = -0.1538461538
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