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Simplifying lg(x + 3) + lg(x + -3) = lg(x + 9) Reorder the terms: gl(3 + x) + lg(x + -3) = lg(x + 9) (3 * gl + x * gl) + lg(x + -3) = lg(x + 9) (3gl + glx) + lg(x + -3) = lg(x + 9) Reorder the terms: 3gl + glx + gl(-3 + x) = lg(x + 9) 3gl + glx + (-3 * gl + x * gl) = lg(x + 9) 3gl + glx + (-3gl + glx) = lg(x + 9) Reorder the terms: 3gl + -3gl + glx + glx = lg(x + 9) Combine like terms: 3gl + -3gl = 0 0 + glx + glx = lg(x + 9) glx + glx = lg(x + 9) Combine like terms: glx + glx = 2glx 2glx = lg(x + 9) Reorder the terms: 2glx = gl(9 + x) 2glx = (9 * gl + x * gl) 2glx = (9gl + glx) Solving 2glx = 9gl + glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-9gl' to each side of the equation. -9gl + 2glx = 9gl + -9gl + glx Combine like terms: 9gl + -9gl = 0 -9gl + 2glx = 0 + glx -9gl + 2glx = glx Add '-1glx' to each side of the equation. -9gl + 2glx + -1glx = glx + -1glx Combine like terms: 2glx + -1glx = 1glx -9gl + 1glx = glx + -1glx Combine like terms: glx + -1glx = 0 -9gl + 1glx = 0 Factor out the Greatest Common Factor (GCF), 'gl'. gl(-9 + x) = 0Subproblem 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 '(-9 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Add '-1x' to each side of the equation. x + -1x = 9 + -1x Combine like terms: x + -1x = 0 0 = 9 + -1x Simplifying 0 = 9 + -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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