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Simplifying 4(2p + -3r + 12) + -5(p + r + 11) = 3p + -17r + -7 Reorder the terms: 4(12 + 2p + -3r) + -5(p + r + 11) = 3p + -17r + -7 (12 * 4 + 2p * 4 + -3r * 4) + -5(p + r + 11) = 3p + -17r + -7 (48 + 8p + -12r) + -5(p + r + 11) = 3p + -17r + -7 Reorder the terms: 48 + 8p + -12r + -5(11 + p + r) = 3p + -17r + -7 48 + 8p + -12r + (11 * -5 + p * -5 + r * -5) = 3p + -17r + -7 48 + 8p + -12r + (-55 + -5p + -5r) = 3p + -17r + -7 Reorder the terms: 48 + -55 + 8p + -5p + -12r + -5r = 3p + -17r + -7 Combine like terms: 48 + -55 = -7 -7 + 8p + -5p + -12r + -5r = 3p + -17r + -7 Combine like terms: 8p + -5p = 3p -7 + 3p + -12r + -5r = 3p + -17r + -7 Combine like terms: -12r + -5r = -17r -7 + 3p + -17r = 3p + -17r + -7 Reorder the terms: -7 + 3p + -17r = -7 + 3p + -17r Add '7' to each side of the equation. -7 + 3p + 7 + -17r = -7 + 3p + 7 + -17r Reorder the terms: -7 + 7 + 3p + -17r = -7 + 3p + 7 + -17r Combine like terms: -7 + 7 = 0 0 + 3p + -17r = -7 + 3p + 7 + -17r 3p + -17r = -7 + 3p + 7 + -17r Reorder the terms: 3p + -17r = -7 + 7 + 3p + -17r Combine like terms: -7 + 7 = 0 3p + -17r = 0 + 3p + -17r 3p + -17r = 3p + -17r Add '-3p' to each side of the equation. 3p + -3p + -17r = 3p + -3p + -17r Combine like terms: 3p + -3p = 0 0 + -17r = 3p + -3p + -17r -17r = 3p + -3p + -17r Combine like terms: 3p + -3p = 0 -17r = 0 + -17r -17r = -17r Add '17r' to each side of the equation. -17r + 17r = -17r + 17r Combine like terms: -17r + 17r = 0 0 = -17r + 17r Combine like terms: -17r + 17r = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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