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Simplifying lg(x + 3) = -1lg(2x + 5) Reorder the terms: gl(3 + x) = -1lg(2x + 5) (3 * gl + x * gl) = -1lg(2x + 5) (3gl + glx) = -1lg(2x + 5) Reorder the terms: 3gl + glx = -1gl(5 + 2x) 3gl + glx = (5 * -1gl + 2x * -1gl) 3gl + glx = (-5gl + -2glx) Solving 3gl + glx = -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 + glx = -5gl + 5gl + -2glx Combine like terms: 3gl + 5gl = 8gl 8gl + glx = -5gl + 5gl + -2glx Combine like terms: -5gl + 5gl = 0 8gl + glx = 0 + -2glx 8gl + glx = -2glx Add '2glx' to each side of the equation. 8gl + glx + 2glx = -2glx + 2glx Combine like terms: glx + 2glx = 3glx 8gl + 3glx = -2glx + 2glx Combine like terms: -2glx + 2glx = 0 8gl + 3glx = 0 Factor out the Greatest Common Factor (GCF), 'gl'. gl(8 + 3x) = 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 '(8 + 3x)' equal to zero and attempt to solve: Simplifying 8 + 3x = 0 Solving 8 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 3x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3x = 0 + -8 3x = 0 + -8 Combine like terms: 0 + -8 = -8 3x = -8 Add '-3x' to each side of the equation. 3x + -3x = -8 + -3x Combine like terms: 3x + -3x = 0 0 = -8 + -3x Simplifying 0 = -8 + -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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