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Simplifying (1 + -4r) + -12r = -7(3r + -1) + 9 Remove parenthesis around (1 + -4r) 1 + -4r + -12r = -7(3r + -1) + 9 Combine like terms: -4r + -12r = -16r 1 + -16r = -7(3r + -1) + 9 Reorder the terms: 1 + -16r = -7(-1 + 3r) + 9 1 + -16r = (-1 * -7 + 3r * -7) + 9 1 + -16r = (7 + -21r) + 9 Reorder the terms: 1 + -16r = 7 + 9 + -21r Combine like terms: 7 + 9 = 16 1 + -16r = 16 + -21r Solving 1 + -16r = 16 + -21r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '21r' to each side of the equation. 1 + -16r + 21r = 16 + -21r + 21r Combine like terms: -16r + 21r = 5r 1 + 5r = 16 + -21r + 21r Combine like terms: -21r + 21r = 0 1 + 5r = 16 + 0 1 + 5r = 16 Add '-1' to each side of the equation. 1 + -1 + 5r = 16 + -1 Combine like terms: 1 + -1 = 0 0 + 5r = 16 + -1 5r = 16 + -1 Combine like terms: 16 + -1 = 15 5r = 15 Divide each side by '5'. r = 3 Simplifying r = 3
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