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Simplifying lg(3x + -1) + lg(7x + -5) = 0 Reorder the terms: gl(-1 + 3x) + lg(7x + -5) = 0 (-1 * gl + 3x * gl) + lg(7x + -5) = 0 (-1gl + 3glx) + lg(7x + -5) = 0 Reorder the terms: -1gl + 3glx + gl(-5 + 7x) = 0 -1gl + 3glx + (-5 * gl + 7x * gl) = 0 -1gl + 3glx + (-5gl + 7glx) = 0 Reorder the terms: -1gl + -5gl + 3glx + 7glx = 0 Combine like terms: -1gl + -5gl = -6gl -6gl + 3glx + 7glx = 0 Combine like terms: 3glx + 7glx = 10glx -6gl + 10glx = 0 Solving -6gl + 10glx = 0 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '2gl'. 2gl(-3 + 5x) = 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 '(-3 + 5x)' equal to zero and attempt to solve: Simplifying -3 + 5x = 0 Solving -3 + 5x = 0 Move all terms containing g to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 5x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 5x = 0 + 3 5x = 0 + 3 Combine like terms: 0 + 3 = 3 5x = 3 Add '-5x' to each side of the equation. 5x + -5x = 3 + -5x Combine like terms: 5x + -5x = 0 0 = 3 + -5x Simplifying 0 = 3 + -5x 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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