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Simplifying [2](4x + -2) = log[2](2x + 5) Reorder the terms: 2(-2 + 4x) = log[2](2x + 5) (-2 * 2 + 4x * 2) = log[2](2x + 5) (-4 + 8x) = log[2](2x + 5) Reorder the terms: -4 + 8x = glo * 2(5 + 2x) Reorder the terms for easier multiplication: -4 + 8x = 2glo(5 + 2x) -4 + 8x = (5 * 2glo + 2x * 2glo) -4 + 8x = (10glo + 4glox) Solving -4 + 8x = 10glo + 4glox Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4glox' to each side of the equation. -4 + -4glox + 8x = 10glo + 4glox + -4glox Combine like terms: 4glox + -4glox = 0 -4 + -4glox + 8x = 10glo + 0 -4 + -4glox + 8x = 10glo Add '4' to each side of the equation. -4 + -4glox + 4 + 8x = 4 + 10glo Reorder the terms: -4 + 4 + -4glox + 8x = 4 + 10glo Combine like terms: -4 + 4 = 0 0 + -4glox + 8x = 4 + 10glo -4glox + 8x = 4 + 10glo Reorder the terms: -4 + -10glo + -4glox + 8x = 4 + 10glo + -4 + -10glo Reorder the terms: -4 + -10glo + -4glox + 8x = 4 + -4 + 10glo + -10glo Combine like terms: 4 + -4 = 0 -4 + -10glo + -4glox + 8x = 0 + 10glo + -10glo -4 + -10glo + -4glox + 8x = 10glo + -10glo Combine like terms: 10glo + -10glo = 0 -4 + -10glo + -4glox + 8x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -5glo + -2glox + 4x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -5glo + -2glox + 4x)' equal to zero and attempt to solve: Simplifying -2 + -5glo + -2glox + 4x = 0 Solving -2 + -5glo + -2glox + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + -5glo + -2glox + 2 + 4x = 0 + 2 Reorder the terms: -2 + 2 + -5glo + -2glox + 4x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5glo + -2glox + 4x = 0 + 2 -5glo + -2glox + 4x = 0 + 2 Combine like terms: 0 + 2 = 2 -5glo + -2glox + 4x = 2 Add '5glo' to each side of the equation. -5glo + -2glox + 5glo + 4x = 2 + 5glo Reorder the terms: -5glo + 5glo + -2glox + 4x = 2 + 5glo Combine like terms: -5glo + 5glo = 0 0 + -2glox + 4x = 2 + 5glo -2glox + 4x = 2 + 5glo 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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