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Simplifying 3sin(2x + 80) = sin(x + 80) Reorder the terms: 3ins(80 + 2x) = sin(x + 80) (80 * 3ins + 2x * 3ins) = sin(x + 80) (240ins + 6insx) = sin(x + 80) Reorder the terms: 240ins + 6insx = ins(80 + x) 240ins + 6insx = (80 * ins + x * ins) 240ins + 6insx = (80ins + insx) Solving 240ins + 6insx = 80ins + insx Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-80ins' to each side of the equation. 240ins + -80ins + 6insx = 80ins + -80ins + insx Combine like terms: 240ins + -80ins = 160ins 160ins + 6insx = 80ins + -80ins + insx Combine like terms: 80ins + -80ins = 0 160ins + 6insx = 0 + insx 160ins + 6insx = insx Add '-1insx' to each side of the equation. 160ins + 6insx + -1insx = insx + -1insx Combine like terms: 6insx + -1insx = 5insx 160ins + 5insx = insx + -1insx Combine like terms: insx + -1insx = 0 160ins + 5insx = 0 Factor out the Greatest Common Factor (GCF), '5ins'. 5ins(32 + x) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'ins' equal to zero and attempt to solve: Simplifying ins = 0 Solving ins = 0 Move all terms containing i to the left, all other terms to the right. Simplifying ins = 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 '(32 + x)' equal to zero and attempt to solve: Simplifying 32 + x = 0 Solving 32 + x = 0 Move all terms containing i to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x = 0 + -32 Combine like terms: 32 + -32 = 0 0 + x = 0 + -32 x = 0 + -32 Combine like terms: 0 + -32 = -32 x = -32 Add '-1x' to each side of the equation. x + -1x = -32 + -1x Combine like terms: x + -1x = 0 0 = -32 + -1x Simplifying 0 = -32 + -1x 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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