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Simplifying lg(15x) = lg(x + 4) Remove parenthesis around (15x) gl * 15x = lg(x + 4) Reorder the terms for easier multiplication: 15gl * x = lg(x + 4) Multiply gl * x 15glx = lg(x + 4) Reorder the terms: 15glx = gl(4 + x) 15glx = (4 * gl + x * gl) 15glx = (4gl + glx) Solving 15glx = 4gl + glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-4gl' to each side of the equation. -4gl + 15glx = 4gl + -4gl + glx Combine like terms: 4gl + -4gl = 0 -4gl + 15glx = 0 + glx -4gl + 15glx = glx Add '-1glx' to each side of the equation. -4gl + 15glx + -1glx = glx + -1glx Combine like terms: 15glx + -1glx = 14glx -4gl + 14glx = glx + -1glx Combine like terms: glx + -1glx = 0 -4gl + 14glx = 0 Factor out the Greatest Common Factor (GCF), '2gl'. 2gl(-2 + 7x) = 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 '(-2 + 7x)' equal to zero and attempt to solve: Simplifying -2 + 7x = 0 Solving -2 + 7x = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 7x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 7x = 0 + 2 7x = 0 + 2 Combine like terms: 0 + 2 = 2 7x = 2 Add '-7x' to each side of the equation. 7x + -7x = 2 + -7x Combine like terms: 7x + -7x = 0 0 = 2 + -7x Simplifying 0 = 2 + -7x 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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