Advertisements
Advertisements
प्रश्न
Solve the following system of inequalities `(2x + 1)/(7x - 1) > 5, (x + 7)/(x - 8) > 2`
Advertisements
उत्तर
`(2x + 1)/(7x - 1) > 5`
Subtracting 5 both side, we get
`(2x + 1)/(7x - 1) - 5 > 0`
⇒ `(2x + 1- 35x + 5)/(7x - 1) > 0`
⇒ `(6 - 33x)/(7x - 1) > 0`
For above fraction be greater than 0, either both denominator and numerator should be greater than 0 or both should be less than 0.
⇒ 6 – 33x > 0 and 7x – 1 > 0
⇒ 33x < 6 and 7x > 1
⇒ x < `2/11` and x > `1/7`
⇒ `1/7` < x < `2/11` ......(i)
Or
⇒ 6 – 33x < 0 and 7x – 1 < 0
⇒ 33x > 6 and 7x < 1
⇒ x > `2/11` and x < `1/7`
⇒ `2/11< x < 1/7` ......(Which is not possible since `1/7 > 2/11`)
Also, `(x + 7)/(x - 8) > 2`
Subtracting 2 both sides, we get
⇒ `(x + 7)/(x - 8) - 2 > 0`
⇒ `(x + 7 - 2x + 16)/(x - 8) > 0`
⇒ `(23 - x)/(x - 8) > 0`
For above fraction be greater than 0.
Either both denominator and numerator should be greater than 0 or both should be less than 0.
⇒ 23 – x > 0 and x – 8 > 0
⇒ x < 23 and x > 8
⇒ 8 < x < 23 ......(ii)
Or
23 – x < 0 and x – 8 < 0
⇒ x > 23 and x < 8
⇒ 23 < x < 8 ......(Which is not possible, as 23 > 8]
Therefore, from equations (i) and (ii).
We infer that there is no solution satisfying both inequalities.
Hence, the given system has no solution.
APPEARS IN
संबंधित प्रश्न
Solve the following system of inequalities graphically: x ≥ 3, y ≥ 2
Solve the following system of inequalities graphically: 3x + 2y ≤ 12, x ≥ 1, y ≥ 2
Solve the following system of inequalities graphically: 2x + y≥ 6, 3x + 4y ≤ 12
Solve the following system of inequalities graphically: x + y ≤ 9, y > x, x ≥ 0
Solve the following system of inequalities graphically: 3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0
Solve the following system of inequalities graphically: 2x + y≥ 4, x + y ≤ 3, 2x – 3y ≤ 6
Solve the following system of inequalities graphically: 3x + 2y ≤ 150, x + 4y ≤ 80, x ≤ 15, y ≥ 0, x ≥ 0
Find all pairs of consecutive odd natural number, both of which are larger than 10, such that their sum is less than 40.
The marks scored by Rohit in two tests were 65 and 70. Find the minimum marks he should score in the third test to have an average of at least 65 marks.
To receive grade 'A' in a course, one must obtain an average of 90 marks or more in five papers each of 100 marks. If Shikha scored 87, 95, 92 and 94 marks in first four paper, find the minimum marks that she must score in the last paper to get grade 'A' in the course.
The longest side of a triangle is three times the shortest side and third side is 2 cm shorter than the longest side if the perimeter of the triangles at least 61 cm, find the minimum length of the shortest-side.
How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?
A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If there are 640 litres of the 8% solution, how many litres of 2% solution will have to be added?
The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between 7.2 and 7.8. If the first two pH reading are 7.48 and 7.85, find the range of pH value for the third reading that will result in the acidity level being normal.
Write the set of values of x satisfying the inequation (x2 − 2x + 1) (x − 4) < 0.
Write the solution set of the equation |2 − x| = x − 2.
Write the set of values of x satisfying |x − 1| ≤ 3 and |x − 1| ≥ 1.
Write the number of integral solutions of \[\frac{x + 2}{x^2 + 1} > \frac{1}{2}\]
Write the set of values of x satisfying the inequations 5x + 2 < 3x + 8 and \[\frac{x + 2}{x - 1} < 4\]
Write the solution of set of\[\left| x + \frac{1}{x} \right| > 2\]
Solve each of the following system of equations in R.
\[5x - 7 < 3\left( x + 3 \right), 1 - \frac{3x}{2} \geq x - 4\]
Find the graphical solution of the following system of linear inequations:
x – y ≤ 0, 2x – y ≥ − 2
Find the graphical solution of the following system of linear inequations:
2x + 3y ≥ 12, – x + y ≤ 3, x ≤ 4, y ≥ 3
Find the graphical solution of the following system of linear inequations:
`"x"/60 + "y"/90 ≤ 1`, `"x"/120 + "y"/75 ≤ 1`, y ≥ 0, x ≥ 0
Solve the following system of inequalities graphically.
2x – y ≥ 1, x – 2y ≤ – 1
Show that the following system of linear inequalities has no solution x + 2y ≤ 3, 3x + 4y ≥ 12, x ≥ 0, y ≥ 1
Show that the solution set of the following system of linear inequalities is an unbounded region 2x + y ≥ 8, x + 2y ≥ 10, x ≥ 0, y ≥ 0.
Solution set of x ≥ 0 and y ≤ 1 is
