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Simplifying (4r + -1z) + -1(3r + 1) = 8 Remove parenthesis around (4r + -1z) 4r + -1z + -1(3r + 1) = 8 Reorder the terms: 4r + -1z + -1(1 + 3r) = 8 4r + -1z + (1 * -1 + 3r * -1) = 8 4r + -1z + (-1 + -3r) = 8 Reorder the terms: -1 + 4r + -3r + -1z = 8 Combine like terms: 4r + -3r = 1r -1 + 1r + -1z = 8 Solving -1 + 1r + -1z = 8 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1r + 1 + -1z = 8 + 1 Reorder the terms: -1 + 1 + 1r + -1z = 8 + 1 Combine like terms: -1 + 1 = 0 0 + 1r + -1z = 8 + 1 1r + -1z = 8 + 1 Combine like terms: 8 + 1 = 9 1r + -1z = 9 Add 'z' to each side of the equation. 1r + -1z + z = 9 + z Combine like terms: -1z + z = 0 1r + 0 = 9 + z 1r = 9 + z Divide each side by '1'. r = 9 + z Simplifying r = 9 + z
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