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Simplifying 1 + lg(5x + -2) = lg(2x + 1) Reorder the terms: 1 + gl(-2 + 5x) = lg(2x + 1) 1 + (-2 * gl + 5x * gl) = lg(2x + 1) 1 + (-2gl + 5glx) = lg(2x + 1) Reorder the terms: 1 + -2gl + 5glx = gl(1 + 2x) 1 + -2gl + 5glx = (1 * gl + 2x * gl) 1 + -2gl + 5glx = (1gl + 2glx) Solving 1 + -2gl + 5glx = 1gl + 2glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1gl' to each side of the equation. 1 + -2gl + -1gl + 5glx = 1gl + -1gl + 2glx Combine like terms: -2gl + -1gl = -3gl 1 + -3gl + 5glx = 1gl + -1gl + 2glx Combine like terms: 1gl + -1gl = 0 1 + -3gl + 5glx = 0 + 2glx 1 + -3gl + 5glx = 2glx Add '-2glx' to each side of the equation. 1 + -3gl + 5glx + -2glx = 2glx + -2glx Combine like terms: 5glx + -2glx = 3glx 1 + -3gl + 3glx = 2glx + -2glx Combine like terms: 2glx + -2glx = 0 1 + -3gl + 3glx = 0 Add '-1' to each side of the equation. 1 + -3gl + -1 + 3glx = 0 + -1 Reorder the terms: 1 + -1 + -3gl + 3glx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3gl + 3glx = 0 + -1 -3gl + 3glx = 0 + -1 Combine like terms: 0 + -1 = -1 -3gl + 3glx = -1 Reorder the terms: 1 + -3gl + 3glx = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -3gl + 3glx = 0 The solution to this equation could not be determined.
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