Question
Solve the inequality and represent the solution graphically on number line: 5 (2x – 7) – 3 (2x + 3) $\le$ 0 , 2x + 19 $\le$ 6x + 47.
✓
Answer
We have $5(2x - 7) - 3(2x + 3) \leqslant 0$ and $2x + 19 \leqslant 6x + 47$
$ \Rightarrow 10x - 35 - 6x - 9 \leqslant 0$ and $ - 4x \leqslant 28$
$ \Rightarrow 4x - 44 \leqslant 0$ and $x \geqslant - 7$
$ \Rightarrow 4x \leqslant 44$ and $x \geqslant - 7$
$ \Rightarrow x \leqslant 11$ and $x \geqslant - 7$
$ \Rightarrow 10x - 35 - 6x - 9 \leqslant 0$ and $ - 4x \leqslant 28$
$ \Rightarrow 4x - 44 \leqslant 0$ and $x \geqslant - 7$
$ \Rightarrow 4x \leqslant 44$ and $x \geqslant - 7$
$ \Rightarrow x \leqslant 11$ and $x \geqslant - 7$
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
Evaluate $\lim\limits_{\text{x}\rightarrow0}\text{f(x)},$ where $\text{f(x)}=\begin{cases}\frac{|\text{x}|}{\text{x}}, & \text{x} \ne0\\0, &\text{x} = 0\end{cases}.$
→Find the mean deviation about the mean for the following data.
| Marks obtained | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| Number of students | 2 | 3 | 8 | 14 | 8 | 3 | 2 |
Find the values of the other five trigonometric functions in the following:
$\tan\text{x}=-\frac{3}{4},$ x in quadrant III
→$\tan\text{x}=-\frac{3}{4},$ x in quadrant III
A box contains 10 white, 6 red and 10 black balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either white or red?
The sum of three numbers in A.P. is 12 and the sum of their cubes is 288. Find the numbers.
Find the equation of the straight line upon which the length of the perpendicular from the origin is 2 and the slope of this perpendicular is $\frac{5}{12}.$
→Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5.
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
Find the distance of the point (1, 2) from the straight line with slope 5 and passing through the point of intersection of x + 2y = 5 and x - 3y = 7.
Solve the following linear inequations in R:
$\frac{\text{x}}{\text{x}-5}>\frac{1}{2}$
→$\frac{\text{x}}{\text{x}-5}>\frac{1}{2}$