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Simplifying lg(3x + 17) = lg(x + 1) Reorder the terms: gl(17 + 3x) = lg(x + 1) (17 * gl + 3x * gl) = lg(x + 1) (17gl + 3glx) = lg(x + 1) Reorder the terms: 17gl + 3glx = gl(1 + x) 17gl + 3glx = (1 * gl + x * gl) 17gl + 3glx = (1gl + glx) Solving 17gl + 3glx = 1gl + glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1gl' to each side of the equation. 17gl + -1gl + 3glx = 1gl + -1gl + glx Combine like terms: 17gl + -1gl = 16gl 16gl + 3glx = 1gl + -1gl + glx Combine like terms: 1gl + -1gl = 0 16gl + 3glx = 0 + glx 16gl + 3glx = glx Add '-1glx' to each side of the equation. 16gl + 3glx + -1glx = glx + -1glx Combine like terms: 3glx + -1glx = 2glx 16gl + 2glx = glx + -1glx Combine like terms: glx + -1glx = 0 16gl + 2glx = 0 Factor out the Greatest Common Factor (GCF), '2gl'. 2gl(8 + x) = 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 '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Add '-1x' to each side of the equation. x + -1x = -8 + -1x Combine like terms: x + -1x = 0 0 = -8 + -1x Simplifying 0 = -8 + -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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