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Simplifying lg(9 + -1x) + lg(x) = lg(x + -2) + lg(x + 1) (9 * gl + -1x * gl) + lg(x) = lg(x + -2) + lg(x + 1) (9gl + -1glx) + lg(x) = lg(x + -2) + lg(x + 1) Multiply gl * x 9gl + -1glx + glx = lg(x + -2) + lg(x + 1) Combine like terms: -1glx + glx = 0 9gl + 0 = lg(x + -2) + lg(x + 1) 9gl = lg(x + -2) + lg(x + 1) Reorder the terms: 9gl = gl(-2 + x) + lg(x + 1) 9gl = (-2 * gl + x * gl) + lg(x + 1) 9gl = (-2gl + glx) + lg(x + 1) Reorder the terms: 9gl = -2gl + glx + gl(1 + x) 9gl = -2gl + glx + (1 * gl + x * gl) 9gl = -2gl + glx + (1gl + glx) Reorder the terms: 9gl = -2gl + 1gl + glx + glx Combine like terms: -2gl + 1gl = -1gl 9gl = -1gl + glx + glx Combine like terms: glx + glx = 2glx 9gl = -1gl + 2glx Solving 9gl = -1gl + 2glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add 'gl' to each side of the equation. 9gl + gl = -1gl + gl + 2glx Combine like terms: 9gl + gl = 10gl 10gl = -1gl + gl + 2glx Combine like terms: -1gl + gl = 0 10gl = 0 + 2glx 10gl = 2glx Add '-2glx' to each side of the equation. 10gl + -2glx = 2glx + -2glx Combine like terms: 2glx + -2glx = 0 10gl + -2glx = 0 Factor out the Greatest Common Factor (GCF), '2gl'. 2gl(5 + -1x) = 0 Ignore the factor 2.Subproblem 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 '(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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