need help Prove the following statement.For every real number x, if x − [x] >²1/1/1/1₁Proof: Suppose x is any real number such thatthen [2x]2[x] + 1.X- [x] = 1/2.Multiply both sides of the inequality by 2 to obtain 2x - 2[x] ≥ 1 or, equivalently, --Select---Now by definition of floor, x < [x] + 1, and hence ---Select---(**).Put inequalities (*) and (**) together to obtain 2[x] + 1 ? ✓ 2x ? ✓ ---Select--- ✓Thus, by definition of floor, [2x] = 2[x] + 1.(*).

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Prove the following statement. For every real number x, if x − [x] ≥ 1/1/12 then [2x] = 2[x] + 1. Proof: Suppose x is any real number such that X- <- [x] ²/1/201 2[x] ≥ 1 or, equivalently, -Select--- Multiply both sides of the inequality by 2 to obtain 2x Now by definition of floor, x < [x] + 1, and hence ---Select--- (**). Put inequalities (*) and (**) together to obtain 2[x] + 1 ? 2x ? ✓ ---Select--- Thus, by definition of floor, [2x] = 2[x] + 1.