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Simplifying lg(2x + -5) + -1lg(3x + 1) = 2 Reorder the terms: gl(-5 + 2x) + -1lg(3x + 1) = 2 (-5 * gl + 2x * gl) + -1lg(3x + 1) = 2 (-5gl + 2glx) + -1lg(3x + 1) = 2 Reorder the terms: -5gl + 2glx + -1gl(1 + 3x) = 2 -5gl + 2glx + (1 * -1gl + 3x * -1gl) = 2 -5gl + 2glx + (-1gl + -3glx) = 2 Reorder the terms: -5gl + -1gl + 2glx + -3glx = 2 Combine like terms: -5gl + -1gl = -6gl -6gl + 2glx + -3glx = 2 Combine like terms: 2glx + -3glx = -1glx -6gl + -1glx = 2 Solving -6gl + -1glx = 2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -2 + -6gl + -1glx = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -6gl + -1glx = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 6gl + glx) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 6gl + glx)' equal to zero and attempt to solve: Simplifying 2 + 6gl + glx = 0 Solving 2 + 6gl + glx = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + 6gl + -2 + glx = 0 + -2 Reorder the terms: 2 + -2 + 6gl + glx = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 6gl + glx = 0 + -2 6gl + glx = 0 + -2 Combine like terms: 0 + -2 = -2 6gl + glx = -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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