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Simplifying 1 + 0.5lg(2x + -1) = lg(4x + -2) Reorder the terms: 1 + 0.5gl(-1 + 2x) = lg(4x + -2) 1 + (-1 * 0.5gl + 2x * 0.5gl) = lg(4x + -2) 1 + (-0.5gl + 1glx) = lg(4x + -2) Reorder the terms: 1 + -0.5gl + 1glx = gl(-2 + 4x) 1 + -0.5gl + 1glx = (-2 * gl + 4x * gl) 1 + -0.5gl + 1glx = (-2gl + 4glx) Solving 1 + -0.5gl + 1glx = -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. 1 + -0.5gl + 2gl + 1glx = -2gl + 2gl + 4glx Combine like terms: -0.5gl + 2gl = 1.5gl 1 + 1.5gl + 1glx = -2gl + 2gl + 4glx Combine like terms: -2gl + 2gl = 0 1 + 1.5gl + 1glx = 0 + 4glx 1 + 1.5gl + 1glx = 4glx Add '-4glx' to each side of the equation. 1 + 1.5gl + 1glx + -4glx = 4glx + -4glx Combine like terms: 1glx + -4glx = -3glx 1 + 1.5gl + -3glx = 4glx + -4glx Combine like terms: 4glx + -4glx = 0 1 + 1.5gl + -3glx = 0 Add '-1' to each side of the equation. 1 + 1.5gl + -1 + -3glx = 0 + -1 Reorder the terms: 1 + -1 + 1.5gl + -3glx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1.5gl + -3glx = 0 + -1 1.5gl + -3glx = 0 + -1 Combine like terms: 0 + -1 = -1 1.5gl + -3glx = -1 Reorder the terms: 1 + 1.5gl + -3glx = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 1.5gl + -3glx = 0 The solution to this equation could not be determined.
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