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Simplifying (x + 1)(a + 4) + 5(a + 4) = (a + 4)(x + 1 + 5) Reorder the terms: (1 + x)(a + 4) + 5(a + 4) = (a + 4)(x + 1 + 5) Reorder the terms: (1 + x)(4 + a) + 5(a + 4) = (a + 4)(x + 1 + 5) Multiply (1 + x) * (4 + a) (1(4 + a) + x(4 + a)) + 5(a + 4) = (a + 4)(x + 1 + 5) ((4 * 1 + a * 1) + x(4 + a)) + 5(a + 4) = (a + 4)(x + 1 + 5) ((4 + 1a) + x(4 + a)) + 5(a + 4) = (a + 4)(x + 1 + 5) (4 + 1a + (4 * x + a * x)) + 5(a + 4) = (a + 4)(x + 1 + 5) Reorder the terms: (4 + 1a + (ax + 4x)) + 5(a + 4) = (a + 4)(x + 1 + 5) (4 + 1a + (ax + 4x)) + 5(a + 4) = (a + 4)(x + 1 + 5) (4 + 1a + ax + 4x) + 5(a + 4) = (a + 4)(x + 1 + 5) Reorder the terms: 4 + 1a + ax + 4x + 5(4 + a) = (a + 4)(x + 1 + 5) 4 + 1a + ax + 4x + (4 * 5 + a * 5) = (a + 4)(x + 1 + 5) 4 + 1a + ax + 4x + (20 + 5a) = (a + 4)(x + 1 + 5) Reorder the terms: 4 + 20 + 1a + 5a + ax + 4x = (a + 4)(x + 1 + 5) Combine like terms: 4 + 20 = 24 24 + 1a + 5a + ax + 4x = (a + 4)(x + 1 + 5) Combine like terms: 1a + 5a = 6a 24 + 6a + ax + 4x = (a + 4)(x + 1 + 5) Reorder the terms: 24 + 6a + ax + 4x = (4 + a)(x + 1 + 5) Reorder the terms: 24 + 6a + ax + 4x = (4 + a)(1 + 5 + x) Combine like terms: 1 + 5 = 6 24 + 6a + ax + 4x = (4 + a)(6 + x) Multiply (4 + a) * (6 + x) 24 + 6a + ax + 4x = (4(6 + x) + a(6 + x)) 24 + 6a + ax + 4x = ((6 * 4 + x * 4) + a(6 + x)) 24 + 6a + ax + 4x = ((24 + 4x) + a(6 + x)) 24 + 6a + ax + 4x = (24 + 4x + (6 * a + x * a)) 24 + 6a + ax + 4x = (24 + 4x + (6a + ax)) Reorder the terms: 24 + 6a + ax + 4x = (24 + 6a + ax + 4x) 24 + 6a + ax + 4x = (24 + 6a + ax + 4x) Add '-24' to each side of the equation. 24 + 6a + ax + -24 + 4x = 24 + 6a + ax + -24 + 4x Reorder the terms: 24 + -24 + 6a + ax + 4x = 24 + 6a + ax + -24 + 4x Combine like terms: 24 + -24 = 0 0 + 6a + ax + 4x = 24 + 6a + ax + -24 + 4x 6a + ax + 4x = 24 + 6a + ax + -24 + 4x Reorder the terms: 6a + ax + 4x = 24 + -24 + 6a + ax + 4x Combine like terms: 24 + -24 = 0 6a + ax + 4x = 0 + 6a + ax + 4x 6a + ax + 4x = 6a + ax + 4x Add '-6a' to each side of the equation. 6a + ax + -6a + 4x = 6a + ax + -6a + 4x Reorder the terms: 6a + -6a + ax + 4x = 6a + ax + -6a + 4x Combine like terms: 6a + -6a = 0 0 + ax + 4x = 6a + ax + -6a + 4x ax + 4x = 6a + ax + -6a + 4x Reorder the terms: ax + 4x = 6a + -6a + ax + 4x Combine like terms: 6a + -6a = 0 ax + 4x = 0 + ax + 4x ax + 4x = ax + 4x Add '-1ax' to each side of the equation. ax + -1ax + 4x = ax + -1ax + 4x Combine like terms: ax + -1ax = 0 0 + 4x = ax + -1ax + 4x 4x = ax + -1ax + 4x Combine like terms: ax + -1ax = 0 4x = 0 + 4x 4x = 4x Add '-4x' to each side of the equation. 4x + -4x = 4x + -4x Combine like terms: 4x + -4x = 0 0 = 4x + -4x Combine like terms: 4x + -4x = 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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