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Simplifying abs(15x + -7) = 5abs(x + 3) Reorder the terms: abs(-7 + 15x) = 5abs(x + 3) (-7 * abs + 15x * abs) = 5abs(x + 3) (-7abs + 15absx) = 5abs(x + 3) Reorder the terms: -7abs + 15absx = 5abs(3 + x) -7abs + 15absx = (3 * 5abs + x * 5abs) -7abs + 15absx = (15abs + 5absx) Solving -7abs + 15absx = 15abs + 5absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-15abs' to each side of the equation. -7abs + -15abs + 15absx = 15abs + -15abs + 5absx Combine like terms: -7abs + -15abs = -22abs -22abs + 15absx = 15abs + -15abs + 5absx Combine like terms: 15abs + -15abs = 0 -22abs + 15absx = 0 + 5absx -22abs + 15absx = 5absx Add '-5absx' to each side of the equation. -22abs + 15absx + -5absx = 5absx + -5absx Combine like terms: 15absx + -5absx = 10absx -22abs + 10absx = 5absx + -5absx Combine like terms: 5absx + -5absx = 0 -22abs + 10absx = 0 Factor out the Greatest Common Factor (GCF), '2abs'. 2abs(-11 + 5x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'abs' equal to zero and attempt to solve: Simplifying abs = 0 Solving abs = 0 Move all terms containing a to the left, all other terms to the right. Simplifying abs = 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 '(-11 + 5x)' equal to zero and attempt to solve: Simplifying -11 + 5x = 0 Solving -11 + 5x = 0 Move all terms containing a to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 5x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 5x = 0 + 11 5x = 0 + 11 Combine like terms: 0 + 11 = 11 5x = 11 Add '-5x' to each side of the equation. 5x + -5x = 11 + -5x Combine like terms: 5x + -5x = 0 0 = 11 + -5x Simplifying 0 = 11 + -5x 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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