Question

como resolver essa inequação:

(2m+1)2 ≤ 4 (m+1)+9

Answer 1

(2m + 1)(2m + 1) = 4m + 2 Reorder the terms: (1 + 2m)(2m + 1) = 4m + 2 Reorder the terms: (1 + 2m)(1 + 2m) = 4m + 2 Multiply (1 + 2m) * (1 + 2m) (1(1 + 2m) + 2m * (1 + 2m)) = 4m + 2 ((1 * 1 + 2m * 1) + 2m * (1 + 2m)) = 4m + 2 ((1 + 2m) + 2m * (1 + 2m)) = 4m + 2 (1 + 2m + (1 * 2m + 2m * 2m)) = 4m + 2 (1 + 2m + (2m + 4m2)) = 4m + 2 Combine like terms: 2m + 2m = 4m (1 + 4m + 4m2) = 4m + 2 Reorder the terms: 1 + 4m + 4m2 = 2 + 4m Add '-4m' to each side of the equation. 1 + 4m + -4m + 4m2 = 2 + 4m + -4m Combine like terms: 4m + -4m = 0 1 + 0 + 4m2 = 2 + 4m + -4m 1 + 4m2 = 2 + 4m + -4m Combine like terms: 4m + -4m = 0 1 + 4m2 = 2 + 0 1 + 4m2 = 2 Solving 1 + 4m2 = 2 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4m2 = 2 + -1 Combine like terms: 1 + -1 = 0 0 + 4m2 = 2 + -1 4m2 = 2 + -1 Combine like terms: 2 + -1 = 1 4m2 = 1 Divide each side by '4'. m2 = 0.25 Simplifying m2 = 0.25 Reorder the terms: -0.25 + m2 = 0.25 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 -0.25 + m2 = 0.00 Factor a difference between two squares. (0.5 + m)(-0.5 + m) = 0.00