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Simplifying 2x + -3(5x + 1) + 4(x + -3) = 7 + -5(x + 2) Reorder the terms: 2x + -3(1 + 5x) + 4(x + -3) = 7 + -5(x + 2) 2x + (1 * -3 + 5x * -3) + 4(x + -3) = 7 + -5(x + 2) 2x + (-3 + -15x) + 4(x + -3) = 7 + -5(x + 2) Reorder the terms: 2x + -3 + -15x + 4(-3 + x) = 7 + -5(x + 2) 2x + -3 + -15x + (-3 * 4 + x * 4) = 7 + -5(x + 2) 2x + -3 + -15x + (-12 + 4x) = 7 + -5(x + 2) Reorder the terms: -3 + -12 + 2x + -15x + 4x = 7 + -5(x + 2) Combine like terms: -3 + -12 = -15 -15 + 2x + -15x + 4x = 7 + -5(x + 2) Combine like terms: 2x + -15x = -13x -15 + -13x + 4x = 7 + -5(x + 2) Combine like terms: -13x + 4x = -9x -15 + -9x = 7 + -5(x + 2) Reorder the terms: -15 + -9x = 7 + -5(2 + x) -15 + -9x = 7 + (2 * -5 + x * -5) -15 + -9x = 7 + (-10 + -5x) Combine like terms: 7 + -10 = -3 -15 + -9x = -3 + -5x Solving -15 + -9x = -3 + -5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5x' to each side of the equation. -15 + -9x + 5x = -3 + -5x + 5x Combine like terms: -9x + 5x = -4x -15 + -4x = -3 + -5x + 5x Combine like terms: -5x + 5x = 0 -15 + -4x = -3 + 0 -15 + -4x = -3 Add '15' to each side of the equation. -15 + 15 + -4x = -3 + 15 Combine like terms: -15 + 15 = 0 0 + -4x = -3 + 15 -4x = -3 + 15 Combine like terms: -3 + 15 = 12 -4x = 12 Divide each side by '-4'. x = -3 Simplifying x = -3
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