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Simplifying lg(x + -1) + -1lg(x + -1) = 1 + -1lg(2x + -10) Reorder the terms: gl(-1 + x) + -1lg(x + -1) = 1 + -1lg(2x + -10) (-1 * gl + x * gl) + -1lg(x + -1) = 1 + -1lg(2x + -10) (-1gl + glx) + -1lg(x + -1) = 1 + -1lg(2x + -10) Reorder the terms: -1gl + glx + -1gl(-1 + x) = 1 + -1lg(2x + -10) -1gl + glx + (-1 * -1gl + x * -1gl) = 1 + -1lg(2x + -10) -1gl + glx + (1gl + -1glx) = 1 + -1lg(2x + -10) Reorder the terms: -1gl + 1gl + glx + -1glx = 1 + -1lg(2x + -10) Combine like terms: -1gl + 1gl = 0 0 + glx + -1glx = 1 + -1lg(2x + -10) glx + -1glx = 1 + -1lg(2x + -10) Combine like terms: glx + -1glx = 0 0 = 1 + -1lg(2x + -10) Reorder the terms: 0 = 1 + -1gl(-10 + 2x) 0 = 1 + (-10 * -1gl + 2x * -1gl) 0 = 1 + (10gl + -2glx) Solving 0 = 1 + 10gl + -2glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-10gl' to each side of the equation. 0 + -10gl = 1 + 10gl + -10gl + -2glx Remove the zero: -10gl = 1 + 10gl + -10gl + -2glx Combine like terms: 10gl + -10gl = 0 -10gl = 1 + 0 + -2glx -10gl = 1 + -2glx Add '2glx' to each side of the equation. -10gl + 2glx = 1 + -2glx + 2glx Combine like terms: -2glx + 2glx = 0 -10gl + 2glx = 1 + 0 -10gl + 2glx = 1 Reorder the terms: -1 + -10gl + 2glx = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -10gl + 2glx = 0 The solution to this equation could not be determined.
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