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Simplifying lg(4x + -5) = lg(5x + 2) Reorder the terms: gl(-5 + 4x) = lg(5x + 2) (-5 * gl + 4x * gl) = lg(5x + 2) (-5gl + 4glx) = lg(5x + 2) Reorder the terms: -5gl + 4glx = gl(2 + 5x) -5gl + 4glx = (2 * gl + 5x * gl) -5gl + 4glx = (2gl + 5glx) Solving -5gl + 4glx = 2gl + 5glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2gl' to each side of the equation. -5gl + -2gl + 4glx = 2gl + -2gl + 5glx Combine like terms: -5gl + -2gl = -7gl -7gl + 4glx = 2gl + -2gl + 5glx Combine like terms: 2gl + -2gl = 0 -7gl + 4glx = 0 + 5glx -7gl + 4glx = 5glx Add '-5glx' to each side of the equation. -7gl + 4glx + -5glx = 5glx + -5glx Combine like terms: 4glx + -5glx = -1glx -7gl + -1glx = 5glx + -5glx Combine like terms: 5glx + -5glx = 0 -7gl + -1glx = 0 Factor out the Greatest Common Factor (GCF), '-1gl'. -1gl(7 + x) = 0 Ignore the factor -1.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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -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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