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Simplifying a(5x + 1) + b(2x + -3) = 4x + 11 Reorder the terms: a(1 + 5x) + b(2x + -3) = 4x + 11 (1 * a + 5x * a) + b(2x + -3) = 4x + 11 (1a + 5ax) + b(2x + -3) = 4x + 11 Reorder the terms: 1a + 5ax + b(-3 + 2x) = 4x + 11 1a + 5ax + (-3 * b + 2x * b) = 4x + 11 1a + 5ax + (-3b + 2bx) = 4x + 11 Reorder the terms: 1a + 5ax + -3b + 2bx = 11 + 4x Solving 1a + 5ax + -3b + 2bx = 11 + 4x Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. 1a + 5ax + -3b + 3b + 2bx = 11 + 3b + 4x Combine like terms: -3b + 3b = 0 1a + 5ax + 0 + 2bx = 11 + 3b + 4x 1a + 5ax + 2bx = 11 + 3b + 4x Add '-2bx' to each side of the equation. 1a + 5ax + 2bx + -2bx = 11 + 3b + -2bx + 4x Combine like terms: 2bx + -2bx = 0 1a + 5ax + 0 = 11 + 3b + -2bx + 4x 1a + 5ax = 11 + 3b + -2bx + 4x Reorder the terms: -11 + 1a + 5ax + -3b + 2bx + -4x = 11 + 3b + -2bx + 4x + -11 + -3b + 2bx + -4x Reorder the terms: -11 + 1a + 5ax + -3b + 2bx + -4x = 11 + -11 + 3b + -3b + -2bx + 2bx + 4x + -4x Combine like terms: 11 + -11 = 0 -11 + 1a + 5ax + -3b + 2bx + -4x = 0 + 3b + -3b + -2bx + 2bx + 4x + -4x -11 + 1a + 5ax + -3b + 2bx + -4x = 3b + -3b + -2bx + 2bx + 4x + -4x Combine like terms: 3b + -3b = 0 -11 + 1a + 5ax + -3b + 2bx + -4x = 0 + -2bx + 2bx + 4x + -4x -11 + 1a + 5ax + -3b + 2bx + -4x = -2bx + 2bx + 4x + -4x Combine like terms: -2bx + 2bx = 0 -11 + 1a + 5ax + -3b + 2bx + -4x = 0 + 4x + -4x -11 + 1a + 5ax + -3b + 2bx + -4x = 4x + -4x Combine like terms: 4x + -4x = 0 -11 + 1a + 5ax + -3b + 2bx + -4x = 0 The solution to this equation could not be determined.
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