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Simplifying logx + 1(x + -0.5) = logx + -0.5(x + 1) Reorder the terms: glox + 1(-0.5 + x) = logx + -0.5(x + 1) glox + (-0.5 * 1 + x * 1) = logx + -0.5(x + 1) glox + (-0.5 + 1x) = logx + -0.5(x + 1) Reorder the terms: -0.5 + glox + 1x = logx + -0.5(x + 1) Reorder the terms: -0.5 + glox + 1x = glox + -0.5(1 + x) -0.5 + glox + 1x = glox + (1 * -0.5 + x * -0.5) -0.5 + glox + 1x = glox + (-0.5 + -0.5x) Reorder the terms: -0.5 + glox + 1x = -0.5 + glox + -0.5x Add '0.5' to each side of the equation. -0.5 + glox + 0.5 + 1x = -0.5 + glox + 0.5 + -0.5x Reorder the terms: -0.5 + 0.5 + glox + 1x = -0.5 + glox + 0.5 + -0.5x Combine like terms: -0.5 + 0.5 = 0.0 0.0 + glox + 1x = -0.5 + glox + 0.5 + -0.5x glox + 1x = -0.5 + glox + 0.5 + -0.5x Reorder the terms: glox + 1x = -0.5 + 0.5 + glox + -0.5x Combine like terms: -0.5 + 0.5 = 0.0 glox + 1x = 0.0 + glox + -0.5x glox + 1x = glox + -0.5x Add '-1glox' to each side of the equation. glox + -1glox + 1x = glox + -1glox + -0.5x Combine like terms: glox + -1glox = 0 0 + 1x = glox + -1glox + -0.5x 1x = glox + -1glox + -0.5x Combine like terms: glox + -1glox = 0 1x = 0 + -0.5x 1x = -0.5x Solving 1x = -0.5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5x' to each side of the equation. 1x + 0.5x = -0.5x + 0.5x Combine like terms: 1x + 0.5x = 1.5x 1.5x = -0.5x + 0.5x Combine like terms: -0.5x + 0.5x = 0.0 1.5x = 0.0 Divide each side by '1.5'. x = 0 Simplifying x = 0
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