MCQ
Solving $ – 8 \leq 5\text{x} – 3<7, $ we get:
- A$\frac{–1}{2}\leq \text{x}\leq 2$
- B$1\leq \text{x}<2$
- ✓$ –1\leq\text{x}<2$
- D$ –1<\text{x}\leq2$
✓
Answer
Correct option: C.
$ –1\leq\text{x}<2$
Given,
$-8\leq5\text{x}-3$ and $5\text{x}-3<7$
Let us solve these two inequalities simultaneously.
$-8\leq5\text{x}-3$ and $5\text{x}-3<7$ can be written as:
$– 8\leq5\text{x} –3 < 7$
Adding 3, we get
$– 8 + 3\leq5\text{x}-3+3<7+3$
$–5\leq5\text{x}<10$
Dividing by 5, we get
$–1\leq\text{x}<2$
$-8\leq5\text{x}-3$ and $5\text{x}-3<7$
Let us solve these two inequalities simultaneously.
$-8\leq5\text{x}-3$ and $5\text{x}-3<7$ can be written as:
$– 8\leq5\text{x} –3 < 7$
Adding 3, we get
$– 8 + 3\leq5\text{x}-3+3<7+3$
$–5\leq5\text{x}<10$
Dividing by 5, we get
$–1\leq\text{x}<2$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If for the complex numbers $z$ satisfying $|z-2-2 i| \leq 1$, the maximum value of $|3 i z+6|$ is attained at $\mathrm{a}+i \mathrm{~b}$, then $\mathrm{a}+\mathrm{b}$ is equal to .... .
→The mean of the following data is :
45, 35, 20, 30, 15, 25, 40:
45, 35, 20, 30, 15, 25, 40:
Circle ${x^2} + {y^2} + 6y = 0$ touches
→Let the positive integers be written in the form :
→$Image$
If the $\mathrm{k}^{\text {th }}$ row contains exactly $\mathrm{k}$ numbers for every natural number $\mathrm{k}$, then the row in which the number $5310$ will be, is.........
If A, B, C are three mutually exclusive and exhaustive events of an experiment such that 3 $\text{P(A)}=2\text{P(B)}=\text{C},$ then P(A) is equal to:
→If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is
The tangent to the parabola ${y^2} = 4ax$ at the point $(a, 2a)$ makes with $x$ - axis an angle equal to
→If ${^\text{m}}\text{C}_{\text{1}}={^\text{n}}\text{C}_{\text{2}},$ is then:
→$\mathop {\lim }\limits_{n \to \infty } {\left( {\frac{n}{{n + y}}} \right)^n}$ equals
→$\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {\frac{1}{2}(1 - \cos 2x)} }}{x} = $
→