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Simplifying 8a + b + -2a + 48 = a + 42 + a + 3b Reorder the terms: 48 + 8a + -2a + b = a + 42 + a + 3b Combine like terms: 8a + -2a = 6a 48 + 6a + b = a + 42 + a + 3b Reorder the terms: 48 + 6a + b = 42 + a + a + 3b Combine like terms: a + a = 2a 48 + 6a + b = 42 + 2a + 3b Solving 48 + 6a + b = 42 + 2a + 3b Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2a' to each side of the equation. 48 + 6a + -2a + b = 42 + 2a + -2a + 3b Combine like terms: 6a + -2a = 4a 48 + 4a + b = 42 + 2a + -2a + 3b Combine like terms: 2a + -2a = 0 48 + 4a + b = 42 + 0 + 3b 48 + 4a + b = 42 + 3b Add '-48' to each side of the equation. 48 + 4a + -48 + b = 42 + -48 + 3b Reorder the terms: 48 + -48 + 4a + b = 42 + -48 + 3b Combine like terms: 48 + -48 = 0 0 + 4a + b = 42 + -48 + 3b 4a + b = 42 + -48 + 3b Combine like terms: 42 + -48 = -6 4a + b = -6 + 3b Add '-1b' to each side of the equation. 4a + b + -1b = -6 + 3b + -1b Combine like terms: b + -1b = 0 4a + 0 = -6 + 3b + -1b 4a = -6 + 3b + -1b Combine like terms: 3b + -1b = 2b 4a = -6 + 2b Divide each side by '4'. a = -1.5 + 0.5b Simplifying a = -1.5 + 0.5b
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