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Simplifying 10(4a + 5b) + -7(7a + 4b) = 0 (4a * 10 + 5b * 10) + -7(7a + 4b) = 0 (40a + 50b) + -7(7a + 4b) = 0 40a + 50b + (7a * -7 + 4b * -7) = 0 40a + 50b + (-49a + -28b) = 0 Reorder the terms: 40a + -49a + 50b + -28b = 0 Combine like terms: 40a + -49a = -9a -9a + 50b + -28b = 0 Combine like terms: 50b + -28b = 22b -9a + 22b = 0 Solving -9a + 22b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-22b' to each side of the equation. -9a + 22b + -22b = 0 + -22b Combine like terms: 22b + -22b = 0 -9a + 0 = 0 + -22b -9a = 0 + -22b Remove the zero: -9a = -22b Divide each side by '-9'. a = 2.444444444b Simplifying a = 2.444444444b
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