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Simplifying 30(a + -2) + -5(4 + -1a) = 40(a + -7) + 194 Reorder the terms: 30(-2 + a) + -5(4 + -1a) = 40(a + -7) + 194 (-2 * 30 + a * 30) + -5(4 + -1a) = 40(a + -7) + 194 (-60 + 30a) + -5(4 + -1a) = 40(a + -7) + 194 -60 + 30a + (4 * -5 + -1a * -5) = 40(a + -7) + 194 -60 + 30a + (-20 + 5a) = 40(a + -7) + 194 Reorder the terms: -60 + -20 + 30a + 5a = 40(a + -7) + 194 Combine like terms: -60 + -20 = -80 -80 + 30a + 5a = 40(a + -7) + 194 Combine like terms: 30a + 5a = 35a -80 + 35a = 40(a + -7) + 194 Reorder the terms: -80 + 35a = 40(-7 + a) + 194 -80 + 35a = (-7 * 40 + a * 40) + 194 -80 + 35a = (-280 + 40a) + 194 Reorder the terms: -80 + 35a = -280 + 194 + 40a Combine like terms: -280 + 194 = -86 -80 + 35a = -86 + 40a Solving -80 + 35a = -86 + 40a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-40a' to each side of the equation. -80 + 35a + -40a = -86 + 40a + -40a Combine like terms: 35a + -40a = -5a -80 + -5a = -86 + 40a + -40a Combine like terms: 40a + -40a = 0 -80 + -5a = -86 + 0 -80 + -5a = -86 Add '80' to each side of the equation. -80 + 80 + -5a = -86 + 80 Combine like terms: -80 + 80 = 0 0 + -5a = -86 + 80 -5a = -86 + 80 Combine like terms: -86 + 80 = -6 -5a = -6 Divide each side by '-5'. a = 1.2 Simplifying a = 1.2
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