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Simplifying lg(x + 7) + lg(x + 1) = 2 Reorder the terms: gl(7 + x) + lg(x + 1) = 2 (7 * gl + x * gl) + lg(x + 1) = 2 (7gl + glx) + lg(x + 1) = 2 Reorder the terms: 7gl + glx + gl(1 + x) = 2 7gl + glx + (1 * gl + x * gl) = 2 7gl + glx + (1gl + glx) = 2 Reorder the terms: 7gl + 1gl + glx + glx = 2 Combine like terms: 7gl + 1gl = 8gl 8gl + glx + glx = 2 Combine like terms: glx + glx = 2glx 8gl + 2glx = 2 Solving 8gl + 2glx = 2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -2 + 8gl + 2glx = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 8gl + 2glx = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 4gl + glx) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 4gl + glx)' equal to zero and attempt to solve: Simplifying -1 + 4gl + glx = 0 Solving -1 + 4gl + glx = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 4gl + 1 + glx = 0 + 1 Reorder the terms: -1 + 1 + 4gl + glx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4gl + glx = 0 + 1 4gl + glx = 0 + 1 Combine like terms: 0 + 1 = 1 4gl + glx = 1 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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