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Simplifying lg(4x + -1) + -1lg(2x + 1) = 2 Reorder the terms: gl(-1 + 4x) + -1lg(2x + 1) = 2 (-1 * gl + 4x * gl) + -1lg(2x + 1) = 2 (-1gl + 4glx) + -1lg(2x + 1) = 2 Reorder the terms: -1gl + 4glx + -1gl(1 + 2x) = 2 -1gl + 4glx + (1 * -1gl + 2x * -1gl) = 2 -1gl + 4glx + (-1gl + -2glx) = 2 Reorder the terms: -1gl + -1gl + 4glx + -2glx = 2 Combine like terms: -1gl + -1gl = -2gl -2gl + 4glx + -2glx = 2 Combine like terms: 4glx + -2glx = 2glx -2gl + 2glx = 2 Solving -2gl + 2glx = 2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -2 + -2gl + 2glx = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -2gl + 2glx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -1gl + glx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -1gl + glx)' equal to zero and attempt to solve: Simplifying -1 + -1gl + glx = 0 Solving -1 + -1gl + glx = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -1gl + 1 + glx = 0 + 1 Reorder the terms: -1 + 1 + -1gl + glx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1gl + glx = 0 + 1 -1gl + glx = 0 + 1 Combine like terms: 0 + 1 = 1 -1gl + glx = 1 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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