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Simplifying lg(x + 3) + lg(1 + -1x) = lg(4x + 8) Reorder the terms: gl(3 + x) + lg(1 + -1x) = lg(4x + 8) (3 * gl + x * gl) + lg(1 + -1x) = lg(4x + 8) (3gl + glx) + lg(1 + -1x) = lg(4x + 8) 3gl + glx + (1 * gl + -1x * gl) = lg(4x + 8) 3gl + glx + (1gl + -1glx) = lg(4x + 8) Reorder the terms: 3gl + 1gl + glx + -1glx = lg(4x + 8) Combine like terms: 3gl + 1gl = 4gl 4gl + glx + -1glx = lg(4x + 8) Combine like terms: glx + -1glx = 0 4gl + 0 = lg(4x + 8) 4gl = lg(4x + 8) Reorder the terms: 4gl = gl(8 + 4x) 4gl = (8 * gl + 4x * gl) 4gl = (8gl + 4glx) Solving 4gl = 8gl + 4glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-8gl' to each side of the equation. 4gl + -8gl = 8gl + -8gl + 4glx Combine like terms: 4gl + -8gl = -4gl -4gl = 8gl + -8gl + 4glx Combine like terms: 8gl + -8gl = 0 -4gl = 0 + 4glx -4gl = 4glx Add '-4glx' to each side of the equation. -4gl + -4glx = 4glx + -4glx Combine like terms: 4glx + -4glx = 0 -4gl + -4glx = 0 Factor out the Greatest Common Factor (GCF), '-4gl'. -4gl(1 + x) = 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x 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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