Question
Solve the following linear in-equation and graph the solution set on a real number line:
$4 \frac{3}{4} \geq x +\frac{5}{6}>\frac{1}{3}, x \in R$
$4 \frac{3}{4} \geq x +\frac{5}{6}>\frac{1}{3}, x \in R$
✓
Answer
$4 \frac{3}{4} \geq x+\frac{5}{6} $
$ \frac{19}{4} \geq \frac{6 x+5}{6} $
$ 114 \geq 24 x+20 $
$114-20 \geq 24 x$
$ 94 \geq 24 x$
$x \leq 3 \frac{11}{12} $
$ \text { and }$
$x+\frac{5}{6}>\frac{1}{3} $
$ \frac{6 x+5}{6}>\frac{1}{3}$
$18 x+15>6$
$18 x>6-15$
$18 x>-9$
$x>-\frac{1}{2}$
Solution set $=\left[-\frac{1}{2}< x \leq 3 \frac{11}{12}\right]$
$ \frac{19}{4} \geq \frac{6 x+5}{6} $
$ 114 \geq 24 x+20 $
$114-20 \geq 24 x$
$ 94 \geq 24 x$
$x \leq 3 \frac{11}{12} $
$ \text { and }$
$x+\frac{5}{6}>\frac{1}{3} $
$ \frac{6 x+5}{6}>\frac{1}{3}$
$18 x+15>6$
$18 x>6-15$
$18 x>-9$
$x>-\frac{1}{2}$
Solution set $=\left[-\frac{1}{2}< x \leq 3 \frac{11}{12}\right]$
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
Prove the following identitie:
$\frac{\sin A-\cos A+1}{\sin A+\cos A-1}=\frac{\cos A}{1-\sin A}$
→$\frac{\sin A-\cos A+1}{\sin A+\cos A-1}=\frac{\cos A}{1-\sin A}$
ABCD is a cyclic quadrilateral of a circle with centre O such that AB is a diameter of this circle and the length of the chord CD is equal to the radius of the circle. If AD and BC produced meet at P, Show that APB = 60°
In the figure; $PA$ is a tangent to the circle, $PBC$ is secant and $AD$ bisects angle BAC. Show that triangle PAD is an isosceles triangle. Also, show that:
$
\angle C A D=\frac{1}{2}(\angle P B A-\angle P A B)
$
→$
\angle C A D=\frac{1}{2}(\angle P B A-\angle P A B)
$
Using ruler and compasses only, construct a triangle ABC in which AB=S cm, BC=6 cm and CA=4.5 cm. Construct a circle passing through A, Band c.
From the data given below . calculate the mean wage, correct to the nnearst rupee.
(1) If the number of workers in each category is doubled, , what would be the new mean wage?
(2) If the wages per day in each category are incresed by 60% what is the new mean wages?
(3) If the number of workers in each caategory is doubled is and the wages per day worker are reduced by 40%, what would be the new mean wage?
| category | A | B | C | D | E | F |
| Wages (Rs,day)(x) | 50 | 60 | 70 | 80 | 90 | 100 |
| no.of workers | 2 | 4 | 8 | 12 | 10 | 6 |
(2) If the wages per day in each category are incresed by 60% what is the new mean wages?
(3) If the number of workers in each caategory is doubled is and the wages per day worker are reduced by 40%, what would be the new mean wage?
The surface area of a solid sphere is increased by $12\%$ without changing its shape. Find the percentage increase in its: radius .
→Draw an ogive for the following :
| Class Interval | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 |
| Frequency | 28 | 23 | 15 | 20 | 14 |
The radius of a solid right circular cylinder decreases by $20\%$ and its height increases by $10\%$. Find the percentage change in its : volume
→Construct a ti.PQR, in which PQ=S. 5 cm, QR=3. 2 cm and PR=4.8 cm. Draw the locus of a point which moves so that it is always 2.5 cm from Q.
A vertical pole and a vertical tower are on the same level ground in such a way that from the top of the pole, the angle of elevation of the top of the tower is $60^\circ$ and the angle of depression of the bottom of the tower is $30^\circ.$ Find: the height of the pole, if the height of the tower is $75 m.$
→