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Simplifying lg(10x + -3) = lg(5 + -2x) Reorder the terms: gl(-3 + 10x) = lg(5 + -2x) (-3 * gl + 10x * gl) = lg(5 + -2x) (-3gl + 10glx) = lg(5 + -2x) -3gl + 10glx = (5 * gl + -2x * gl) -3gl + 10glx = (5gl + -2glx) Solving -3gl + 10glx = 5gl + -2glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5gl' to each side of the equation. -3gl + -5gl + 10glx = 5gl + -5gl + -2glx Combine like terms: -3gl + -5gl = -8gl -8gl + 10glx = 5gl + -5gl + -2glx Combine like terms: 5gl + -5gl = 0 -8gl + 10glx = 0 + -2glx -8gl + 10glx = -2glx Add '2glx' to each side of the equation. -8gl + 10glx + 2glx = -2glx + 2glx Combine like terms: 10glx + 2glx = 12glx -8gl + 12glx = -2glx + 2glx Combine like terms: -2glx + 2glx = 0 -8gl + 12glx = 0 Factor out the Greatest Common Factor (GCF), '4gl'. 4gl(-2 + 3x) = 0 Ignore the factor 4.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 '(-2 + 3x)' equal to zero and attempt to solve: Simplifying -2 + 3x = 0 Solving -2 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 3x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3x = 0 + 2 3x = 0 + 2 Combine like terms: 0 + 2 = 2 3x = 2 Add '-3x' to each side of the equation. 3x + -3x = 2 + -3x Combine like terms: 3x + -3x = 0 0 = 2 + -3x Simplifying 0 = 2 + -3x 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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