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Simplifying 14x(2a + 3b) + -0.5y(2a + 3b) + 4(4a + 6b) = 0 (2a * 14x + 3b * 14x) + -0.5y(2a + 3b) + 4(4a + 6b) = 0 (28ax + 42bx) + -0.5y(2a + 3b) + 4(4a + 6b) = 0 28ax + 42bx + (2a * -0.5y + 3b * -0.5y) + 4(4a + 6b) = 0 28ax + 42bx + (-1ay + -1.5by) + 4(4a + 6b) = 0 28ax + 42bx + -1ay + -1.5by + (4a * 4 + 6b * 4) = 0 28ax + 42bx + -1ay + -1.5by + (16a + 24b) = 0 Reorder the terms: 16a + 28ax + -1ay + 24b + 42bx + -1.5by = 0 Solving 16a + 28ax + -1ay + 24b + 42bx + -1.5by = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-24b' to each side of the equation. 16a + 28ax + -1ay + 24b + 42bx + -24b + -1.5by = 0 + -24b Reorder the terms: 16a + 28ax + -1ay + 24b + -24b + 42bx + -1.5by = 0 + -24b Combine like terms: 24b + -24b = 0 16a + 28ax + -1ay + 0 + 42bx + -1.5by = 0 + -24b 16a + 28ax + -1ay + 42bx + -1.5by = 0 + -24b Remove the zero: 16a + 28ax + -1ay + 42bx + -1.5by = -24b Add '-42bx' to each side of the equation. 16a + 28ax + -1ay + 42bx + -42bx + -1.5by = -24b + -42bx Combine like terms: 42bx + -42bx = 0 16a + 28ax + -1ay + 0 + -1.5by = -24b + -42bx 16a + 28ax + -1ay + -1.5by = -24b + -42bx Add '1.5by' to each side of the equation. 16a + 28ax + -1ay + -1.5by + 1.5by = -24b + -42bx + 1.5by Combine like terms: -1.5by + 1.5by = 0.0 16a + 28ax + -1ay + 0.0 = -24b + -42bx + 1.5by 16a + 28ax + -1ay = -24b + -42bx + 1.5by Reorder the terms: 16a + 28ax + -1ay + 24b + 42bx + -1.5by = -24b + 24b + -42bx + 42bx + 1.5by + -1.5by Combine like terms: -24b + 24b = 0 16a + 28ax + -1ay + 24b + 42bx + -1.5by = 0 + -42bx + 42bx + 1.5by + -1.5by 16a + 28ax + -1ay + 24b + 42bx + -1.5by = -42bx + 42bx + 1.5by + -1.5by Combine like terms: -42bx + 42bx = 0 16a + 28ax + -1ay + 24b + 42bx + -1.5by = 0 + 1.5by + -1.5by 16a + 28ax + -1ay + 24b + 42bx + -1.5by = 1.5by + -1.5by Combine like terms: 1.5by + -1.5by = 0.0 16a + 28ax + -1ay + 24b + 42bx + -1.5by = 0.0 The solution to this equation could not be determined.
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