Question

Which among the following inequality represents the interval [2, ∞)?

(i) x − 3 ≥ 5, x ∈ (ii) 13x − 3 ≥ 5, x ∈ (1)

(iii) 3x − 1 ≥ 3, x ∈ (iv)3x − 1 ≥ 5, x ∈ ​

Answer 1

Answer:

(iv)3x − 1 ≥ 5, x ∈

i think it's help full

Answer 2

Option(iv) is correct.

Concept:

Inequalities are mathematical formulas with two opposing sides. We compare two values via inequality rather than equations. Between the equal signs, a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign is used.

Find:

The inequality that represents the interval $[2, \infty)$.

Solution:

(i)

$x-3\geq 5\\x\geq 8\\x \in [8, \infty)$

(ii)

$13x-3\geq 5\\13x\geq 8\\x\geq \frac{8}{13} \\\\x \in [\frac{8}{13}, \infty)$

(iii)

$3x-1\geq 3\\3x\geq 4\\x\geq \frac{4}{3}\\\\x \in [\frac{4}{3}, \infty)$

(iv)

$3x-1\geq 5\\3x\geq 6\\x\geq 2\\\\x \in [2, \infty)$

Hence, Option(iv) is correct.

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