Prove that for all real x, we have |x−1|+|x + 2|≥ 3.

Solutions

Expert Solution

if u have any questions please comment

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Suppose that x is real number. Prove that x+1/x =2 if and only if x=1. Prove...

Suppose that x is real number. Prove that x+1/x =2 if and only if x=1. Prove that there does not exist a smallest positive real number. Is the result still true if we replace ”real number” with ”integer”? Suppose that x is a real number. Use either proof by contrapositive or proof by contradiction to show that x3 + 5x = 0 implies that x = 0.

Prove that the polynomial x^3 + x^2 – x + 1 has no integer roots

Prove 1. For all A, B ∈ Mmn and scalar a, we have A + B,...

Prove 1. For all A, B ∈ Mmn and scalar a, we have A + B, aA ∈ Mmn. 2. For all A, B ∈ Mmn, A + B = B + A. 3. For all A, B, C ∈ Mmn, (A + B) + C = A + (B + C). 4. For each A ∈ Mmn there is a B ∈ Mmn such that A + B = 0mn.

Prove by contradiction, every real solution of x3+x+3=0 is irrational.

Prove or disprove the statements: (a) If x is a real number such that |x +...

Prove or disprove the statements: (a) If x is a real number such that |x + 2| + |x| ≤ 1, then x 2 + 2x − 1 ≤ 2. (b) If x is a real number such that |x + 2| + |x| ≤ 2, then x 2 + 2x − 1 ≤ 2. (c) If x is a real number such that |x + 2| + |x| ≤ 3, then x 2 + 2x − 1 ≤ 2....

prove that f(x)=x^2019 +x-1 has only one real root

Find the real zeros of the function f(x) = -(x+1)^3(x-2)^2 and their corresponding multiplicities. Use the...

Find the real zeros of the function f(x) = -(x+1)^3(x-2)^2 and their corresponding multiplicities. Use the information along with a sign chart (diagram) and then the end behavior to provide a rough sketch of the graph of the polynomial.

The Polynomial f(x) = X^3 - X^2 - X -1 has one real root a, which...

The Polynomial f(x) = X^3 - X^2 - X -1 has one real root a, which happens to be positive. This real number a satisfies the following properties: - for i = 1,2,3,4,5,6,7,8,9,10, one has {a^i} not equal to zero - one has [a] = 1, [a^2] = 3, [a^3] = 6, [a^4] = 11, [a^5] = 21, [a^6] = 7, [a^7] = 71, [a^8] = 130 (for a real number x, [x] denotes the floor of x and {x}...

The function f(x) = x^2 (x^2 − 2x − 36) is defined on all real numbers....

The function f(x) = x^2 (x^2 − 2x − 36) is defined on all real numbers. On what subset of the real numbers is f(x) concave down?

1. Prove that the Cantor set contains no intervals. 2. Prove: If x is an element...

1. Prove that the Cantor set contains no intervals. 2. Prove: If x is an element of the Cantor set, then there is a sequence Xn of elements from the Cantor set converging to x.

Subjects