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Simplifying 7(5a + -1b) + -7(3ab + -4a) = 0 (5a * 7 + -1b * 7) + -7(3ab + -4a) = 0 (35a + -7b) + -7(3ab + -4a) = 0 Reorder the terms: 35a + -7b + -7(-4a + 3ab) = 0 35a + -7b + (-4a * -7 + 3ab * -7) = 0 35a + -7b + (28a + -21ab) = 0 Reorder the terms: 35a + 28a + -21ab + -7b = 0 Combine like terms: 35a + 28a = 63a 63a + -21ab + -7b = 0 Solving 63a + -21ab + -7b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7b' to each side of the equation. 63a + -21ab + -7b + 7b = 0 + 7b Combine like terms: -7b + 7b = 0 63a + -21ab + 0 = 0 + 7b 63a + -21ab = 0 + 7b Remove the zero: 63a + -21ab = 7b Combine like terms: 7b + -7b = 0 63a + -21ab + -7b = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(9a + -3ab + -1b) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(9a + -3ab + -1b)' equal to zero and attempt to solve: Simplifying 9a + -3ab + -1b = 0 Solving 9a + -3ab + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 9a + -3ab + -1b + b = 0 + b Combine like terms: -1b + b = 0 9a + -3ab + 0 = 0 + b 9a + -3ab = 0 + b Remove the zero: 9a + -3ab = b 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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