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Simplifying lg(6x + -8) + -1lg(2x + 4) = lg(x + -6) Reorder the terms: gl(-8 + 6x) + -1lg(2x + 4) = lg(x + -6) (-8 * gl + 6x * gl) + -1lg(2x + 4) = lg(x + -6) (-8gl + 6glx) + -1lg(2x + 4) = lg(x + -6) Reorder the terms: -8gl + 6glx + -1gl(4 + 2x) = lg(x + -6) -8gl + 6glx + (4 * -1gl + 2x * -1gl) = lg(x + -6) -8gl + 6glx + (-4gl + -2glx) = lg(x + -6) Reorder the terms: -8gl + -4gl + 6glx + -2glx = lg(x + -6) Combine like terms: -8gl + -4gl = -12gl -12gl + 6glx + -2glx = lg(x + -6) Combine like terms: 6glx + -2glx = 4glx -12gl + 4glx = lg(x + -6) Reorder the terms: -12gl + 4glx = gl(-6 + x) -12gl + 4glx = (-6 * gl + x * gl) -12gl + 4glx = (-6gl + glx) Solving -12gl + 4glx = -6gl + glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '6gl' to each side of the equation. -12gl + 6gl + 4glx = -6gl + 6gl + glx Combine like terms: -12gl + 6gl = -6gl -6gl + 4glx = -6gl + 6gl + glx Combine like terms: -6gl + 6gl = 0 -6gl + 4glx = 0 + glx -6gl + 4glx = glx Add '-1glx' to each side of the equation. -6gl + 4glx + -1glx = glx + -1glx Combine like terms: 4glx + -1glx = 3glx -6gl + 3glx = glx + -1glx Combine like terms: glx + -1glx = 0 -6gl + 3glx = 0 Factor out the Greatest Common Factor (GCF), '3gl'. 3gl(-2 + x) = 0 Ignore the factor 3.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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -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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