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Simplifying lg(x2 + -4) = lg(4x + 1) Reorder the terms: gl(-4 + x2) = lg(4x + 1) (-4 * gl + x2 * gl) = lg(4x + 1) (-4gl + glx2) = lg(4x + 1) Reorder the terms: -4gl + glx2 = gl(1 + 4x) -4gl + glx2 = (1 * gl + 4x * gl) -4gl + glx2 = (1gl + 4glx) Solving -4gl + glx2 = 1gl + 4glx 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. -4gl + -1gl + glx2 = 1gl + -1gl + 4glx Combine like terms: -4gl + -1gl = -5gl -5gl + glx2 = 1gl + -1gl + 4glx Combine like terms: 1gl + -1gl = 0 -5gl + glx2 = 0 + 4glx -5gl + glx2 = 4glx Add '-4glx' to each side of the equation. -5gl + -4glx + glx2 = 4glx + -4glx Combine like terms: 4glx + -4glx = 0 -5gl + -4glx + glx2 = 0 Factor out the Greatest Common Factor (GCF), 'gl'. gl(-5 + -4x + x2) = 0 Factor a trinomial. gl((-1 + -1x)(5 + -1x)) = 0Subproblem 1
Set the factor 'gl' equal to zero and attempt to solve: Simplifying gl = 0 Solving gl = 0 Move all terms containing g to the left, all other terms to the right. Simplifying gl = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Add 'x' to each side of the equation. -1x + x = 1 + x Combine like terms: -1x + x = 0 0 = 1 + x Simplifying 0 = 1 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + x 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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