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Simplifying 4(x + -3) + -1r + 2x = 5(3x + -7) + -9x Reorder the terms: 4(-3 + x) + -1r + 2x = 5(3x + -7) + -9x (-3 * 4 + x * 4) + -1r + 2x = 5(3x + -7) + -9x (-12 + 4x) + -1r + 2x = 5(3x + -7) + -9x Reorder the terms: -12 + -1r + 4x + 2x = 5(3x + -7) + -9x Combine like terms: 4x + 2x = 6x -12 + -1r + 6x = 5(3x + -7) + -9x Reorder the terms: -12 + -1r + 6x = 5(-7 + 3x) + -9x -12 + -1r + 6x = (-7 * 5 + 3x * 5) + -9x -12 + -1r + 6x = (-35 + 15x) + -9x Combine like terms: 15x + -9x = 6x -12 + -1r + 6x = -35 + 6x Add '-6x' to each side of the equation. -12 + -1r + 6x + -6x = -35 + 6x + -6x Combine like terms: 6x + -6x = 0 -12 + -1r + 0 = -35 + 6x + -6x -12 + -1r = -35 + 6x + -6x Combine like terms: 6x + -6x = 0 -12 + -1r = -35 + 0 -12 + -1r = -35 Solving -12 + -1r = -35 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1r = -35 + 12 Combine like terms: -12 + 12 = 0 0 + -1r = -35 + 12 -1r = -35 + 12 Combine like terms: -35 + 12 = -23 -1r = -23 Divide each side by '-1'. r = 23 Simplifying r = 23
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