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