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Simplifying 0.66(6a + 3b) + -0.5(a + -2b) = 0 (6a * 0.66 + 3b * 0.66) + -0.5(a + -2b) = 0 (3.96a + 1.98b) + -0.5(a + -2b) = 0 3.96a + 1.98b + (a * -0.5 + -2b * -0.5) = 0 3.96a + 1.98b + (-0.5a + 1b) = 0 Reorder the terms: 3.96a + -0.5a + 1.98b + 1b = 0 Combine like terms: 3.96a + -0.5a = 3.46a 3.46a + 1.98b + 1b = 0 Combine like terms: 1.98b + 1b = 2.98b 3.46a + 2.98b = 0 Solving 3.46a + 2.98b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.98b' to each side of the equation. 3.46a + 2.98b + -2.98b = 0 + -2.98b Combine like terms: 2.98b + -2.98b = 0.00 3.46a + 0.00 = 0 + -2.98b 3.46a = 0 + -2.98b Remove the zero: 3.46a = -2.98b Divide each side by '3.46'. a = -0.8612716763b Simplifying a = -0.8612716763b
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