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Simplifying 1 + 2lg(x + 1) = lg(2x + 1) + lg(5x + 8) Reorder the terms: 1 + 2gl(1 + x) = lg(2x + 1) + lg(5x + 8) 1 + (1 * 2gl + x * 2gl) = lg(2x + 1) + lg(5x + 8) 1 + (2gl + 2glx) = lg(2x + 1) + lg(5x + 8) Reorder the terms: 1 + 2gl + 2glx = gl(1 + 2x) + lg(5x + 8) 1 + 2gl + 2glx = (1 * gl + 2x * gl) + lg(5x + 8) 1 + 2gl + 2glx = (1gl + 2glx) + lg(5x + 8) Reorder the terms: 1 + 2gl + 2glx = 1gl + 2glx + gl(8 + 5x) 1 + 2gl + 2glx = 1gl + 2glx + (8 * gl + 5x * gl) 1 + 2gl + 2glx = 1gl + 2glx + (8gl + 5glx) Reorder the terms: 1 + 2gl + 2glx = 1gl + 8gl + 2glx + 5glx Combine like terms: 1gl + 8gl = 9gl 1 + 2gl + 2glx = 9gl + 2glx + 5glx Combine like terms: 2glx + 5glx = 7glx 1 + 2gl + 2glx = 9gl + 7glx Solving 1 + 2gl + 2glx = 9gl + 7glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-9gl' to each side of the equation. 1 + 2gl + -9gl + 2glx = 9gl + -9gl + 7glx Combine like terms: 2gl + -9gl = -7gl 1 + -7gl + 2glx = 9gl + -9gl + 7glx Combine like terms: 9gl + -9gl = 0 1 + -7gl + 2glx = 0 + 7glx 1 + -7gl + 2glx = 7glx Add '-7glx' to each side of the equation. 1 + -7gl + 2glx + -7glx = 7glx + -7glx Combine like terms: 2glx + -7glx = -5glx 1 + -7gl + -5glx = 7glx + -7glx Combine like terms: 7glx + -7glx = 0 1 + -7gl + -5glx = 0 Add '-1' to each side of the equation. 1 + -7gl + -1 + -5glx = 0 + -1 Reorder the terms: 1 + -1 + -7gl + -5glx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7gl + -5glx = 0 + -1 -7gl + -5glx = 0 + -1 Combine like terms: 0 + -1 = -1 -7gl + -5glx = -1 Reorder the terms: 1 + -7gl + -5glx = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -7gl + -5glx = 0 The solution to this equation could not be determined.
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