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Simplifying lg(x + -1) = lg(5x + -3) Reorder the terms: gl(-1 + x) = lg(5x + -3) (-1 * gl + x * gl) = lg(5x + -3) (-1gl + glx) = lg(5x + -3) Reorder the terms: -1gl + glx = gl(-3 + 5x) -1gl + glx = (-3 * gl + 5x * gl) -1gl + glx = (-3gl + 5glx) Solving -1gl + glx = -3gl + 5glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '3gl' to each side of the equation. -1gl + 3gl + glx = -3gl + 3gl + 5glx Combine like terms: -1gl + 3gl = 2gl 2gl + glx = -3gl + 3gl + 5glx Combine like terms: -3gl + 3gl = 0 2gl + glx = 0 + 5glx 2gl + glx = 5glx Add '-5glx' to each side of the equation. 2gl + glx + -5glx = 5glx + -5glx Combine like terms: glx + -5glx = -4glx 2gl + -4glx = 5glx + -5glx Combine like terms: 5glx + -5glx = 0 2gl + -4glx = 0 Factor out the Greatest Common Factor (GCF), '2gl'. 2gl(1 + -2x) = 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 '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Add '2x' to each side of the equation. -2x + 2x = -1 + 2x Combine like terms: -2x + 2x = 0 0 = -1 + 2x Simplifying 0 = -1 + 2x 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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