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Simplifying lgx + lg(5x + 8) = 2lg(5x + -4) Reorder the terms: glx + gl(8 + 5x) = 2lg(5x + -4) glx + (8 * gl + 5x * gl) = 2lg(5x + -4) glx + (8gl + 5glx) = 2lg(5x + -4) Reorder the terms: 8gl + glx + 5glx = 2lg(5x + -4) Combine like terms: glx + 5glx = 6glx 8gl + 6glx = 2lg(5x + -4) Reorder the terms: 8gl + 6glx = 2gl(-4 + 5x) 8gl + 6glx = (-4 * 2gl + 5x * 2gl) 8gl + 6glx = (-8gl + 10glx) Solving 8gl + 6glx = -8gl + 10glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '8gl' to each side of the equation. 8gl + 8gl + 6glx = -8gl + 8gl + 10glx Combine like terms: 8gl + 8gl = 16gl 16gl + 6glx = -8gl + 8gl + 10glx Combine like terms: -8gl + 8gl = 0 16gl + 6glx = 0 + 10glx 16gl + 6glx = 10glx Add '-10glx' to each side of the equation. 16gl + 6glx + -10glx = 10glx + -10glx Combine like terms: 6glx + -10glx = -4glx 16gl + -4glx = 10glx + -10glx Combine like terms: 10glx + -10glx = 0 16gl + -4glx = 0 Factor out the Greatest Common Factor (GCF), '4gl'. 4gl(4 + -1x) = 0 Ignore the factor 4.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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + x 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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