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Simplifying 7(a * p + 6) + -2 = a(p + -2) + 10 Multiply a * p 7(ap + 6) + -2 = a(p + -2) + 10 Reorder the terms: 7(6 + ap) + -2 = a(p + -2) + 10 (6 * 7 + ap * 7) + -2 = a(p + -2) + 10 (42 + 7ap) + -2 = a(p + -2) + 10 Reorder the terms: 42 + -2 + 7ap = a(p + -2) + 10 Combine like terms: 42 + -2 = 40 40 + 7ap = a(p + -2) + 10 Reorder the terms: 40 + 7ap = a(-2 + p) + 10 40 + 7ap = (-2 * a + p * a) + 10 40 + 7ap = (-2a + ap) + 10 Reorder the terms: 40 + 7ap = 10 + -2a + ap Solving 40 + 7ap = 10 + -2a + ap Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2a' to each side of the equation. 40 + 2a + 7ap = 10 + -2a + 2a + ap Combine like terms: -2a + 2a = 0 40 + 2a + 7ap = 10 + 0 + ap 40 + 2a + 7ap = 10 + ap Add '-1ap' to each side of the equation. 40 + 2a + 7ap + -1ap = 10 + ap + -1ap Combine like terms: 7ap + -1ap = 6ap 40 + 2a + 6ap = 10 + ap + -1ap Combine like terms: ap + -1ap = 0 40 + 2a + 6ap = 10 + 0 40 + 2a + 6ap = 10 Add '-40' to each side of the equation. 40 + 2a + -40 + 6ap = 10 + -40 Reorder the terms: 40 + -40 + 2a + 6ap = 10 + -40 Combine like terms: 40 + -40 = 0 0 + 2a + 6ap = 10 + -40 2a + 6ap = 10 + -40 Combine like terms: 10 + -40 = -30 2a + 6ap = -30 Reorder the terms: 30 + 2a + 6ap = -30 + 30 Combine like terms: -30 + 30 = 0 30 + 2a + 6ap = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + a + 3ap) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + a + 3ap)' equal to zero and attempt to solve: Simplifying 15 + a + 3ap = 0 Solving 15 + a + 3ap = 0 Move all terms containing a to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + a + -15 + 3ap = 0 + -15 Reorder the terms: 15 + -15 + a + 3ap = 0 + -15 Combine like terms: 15 + -15 = 0 0 + a + 3ap = 0 + -15 a + 3ap = 0 + -15 Combine like terms: 0 + -15 = -15 a + 3ap = -15 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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