If b < 2 and 2x - 3b = 0, which of the fo… | Answer

Subject

গাণিতিক যুক্তি

Topic

অসমতা

ক)

x > -3

খ)

x < 2

গ)

x = 3

ঘ)

x < 3

Given the equation

2x - 3b = 0

, we first solve for

x

in terms of

b

2x = 3b

, so

x = \frac{3}{2}b

. Since we are given the condition

b < 2

, we multiply both sides by

\frac{3}{2}

(a positive number) to maintain the inequality direction:

\frac{3}{2}b < \frac{3}{2}(2)

, which simplifies to

x < 3

. Elimination: A ('x > -3') is incorrect because

b

can be negative (e.g., if

b=-4

x=-6

, which is not greater than -3). B ('x < 2') is incorrect because if

b

approaches 2 (e.g.,

b=1.9

x

approaches

2.85

, which is greater than 2. C ('x = 3') is incorrect because

x

must be strictly less than 3, as

b

is strictly less than 2.

\frac{1}{a}

\frac{1}{{{a^{2\;}}}}

If b < 2 and 2x - 3b = 0, which of the following must be true ?