If 4x+3<6x+7 then x belongs to the interval: - Vidyadip

MCQ

If $4\text{x}+3<6\text{x}+7$ then $x$ belongs to the interval:

A
$(2,\infty)$
✓
$(-2,\infty)$
C
$(-\infty, 2)$
D
$(-4,\infty)$

✓

Answer

Correct option: B.

$(-2,\infty)$

$4\text{x}+3<6\text{x}+7$
Subtracting $3$ from both sides,
$4\text{x}+3<6\text{x}+7-3$
$\Rightarrow4\text{x}<6\text{x}+4$
Subtracting $6x$ from both sides,
$4\text{x} – 6\text{x} <6\text{x} + 4 – 6\text{x}$
$\Rightarrow– 2\text{x}<4$ or
$\Rightarrow\text{x}>-2$
$\text{ i.e..,}$ all the real numbers greater than $–2,$ are the solutions of the given inequality.
Hence, the solution set is $(–2,\infty),$
$\text{i}.\text{e}.\text{x}\in(-2,\infty)$

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