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Simplifying lg(7x + -5) = lg(3x + -7) Reorder the terms: gl(-5 + 7x) = lg(3x + -7) (-5 * gl + 7x * gl) = lg(3x + -7) (-5gl + 7glx) = lg(3x + -7) Reorder the terms: -5gl + 7glx = gl(-7 + 3x) -5gl + 7glx = (-7 * gl + 3x * gl) -5gl + 7glx = (-7gl + 3glx) Solving -5gl + 7glx = -7gl + 3glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '7gl' to each side of the equation. -5gl + 7gl + 7glx = -7gl + 7gl + 3glx Combine like terms: -5gl + 7gl = 2gl 2gl + 7glx = -7gl + 7gl + 3glx Combine like terms: -7gl + 7gl = 0 2gl + 7glx = 0 + 3glx 2gl + 7glx = 3glx Add '-3glx' to each side of the equation. 2gl + 7glx + -3glx = 3glx + -3glx Combine like terms: 7glx + -3glx = 4glx 2gl + 4glx = 3glx + -3glx Combine like terms: 3glx + -3glx = 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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