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Simplifying lg(3x + -1) + -1lg(4 + 5x) = 2 Reorder the terms: gl(-1 + 3x) + -1lg(4 + 5x) = 2 (-1 * gl + 3x * gl) + -1lg(4 + 5x) = 2 (-1gl + 3glx) + -1lg(4 + 5x) = 2 -1gl + 3glx + (4 * -1gl + 5x * -1gl) = 2 -1gl + 3glx + (-4gl + -5glx) = 2 Reorder the terms: -1gl + -4gl + 3glx + -5glx = 2 Combine like terms: -1gl + -4gl = -5gl -5gl + 3glx + -5glx = 2 Combine like terms: 3glx + -5glx = -2glx -5gl + -2glx = 2 Solving -5gl + -2glx = 2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -2 + -5gl + -2glx = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -5gl + -2glx = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 5gl + 2glx) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 5gl + 2glx)' equal to zero and attempt to solve: Simplifying 2 + 5gl + 2glx = 0 Solving 2 + 5gl + 2glx = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + 5gl + -2 + 2glx = 0 + -2 Reorder the terms: 2 + -2 + 5gl + 2glx = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5gl + 2glx = 0 + -2 5gl + 2glx = 0 + -2 Combine like terms: 0 + -2 = -2 5gl + 2glx = -2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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