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Simplifying lg(4x + 5) = 1 + lg(x + -1) Reorder the terms: gl(5 + 4x) = 1 + lg(x + -1) (5 * gl + 4x * gl) = 1 + lg(x + -1) (5gl + 4glx) = 1 + lg(x + -1) Reorder the terms: 5gl + 4glx = 1 + gl(-1 + x) 5gl + 4glx = 1 + (-1 * gl + x * gl) 5gl + 4glx = 1 + (-1gl + glx) Solving 5gl + 4glx = 1 + -1gl + glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add 'gl' to each side of the equation. 5gl + gl + 4glx = 1 + -1gl + gl + glx Combine like terms: 5gl + gl = 6gl 6gl + 4glx = 1 + -1gl + gl + glx Combine like terms: -1gl + gl = 0 6gl + 4glx = 1 + 0 + glx 6gl + 4glx = 1 + glx Add '-1glx' to each side of the equation. 6gl + 4glx + -1glx = 1 + glx + -1glx Combine like terms: 4glx + -1glx = 3glx 6gl + 3glx = 1 + glx + -1glx Combine like terms: glx + -1glx = 0 6gl + 3glx = 1 + 0 6gl + 3glx = 1 Reorder the terms: -1 + 6gl + 3glx = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 6gl + 3glx = 0 The solution to this equation could not be determined.
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