Advertisements
Advertisements
Question
Solve each of the following system of equations in R.
2x − 7 > 5 − x, 11 − 5x ≤ 1
Solution
Given as
2x – 7 > 5 – x and 11 – 5x ≤ 1
Now, let us consider the first inequality.
2x – 7 > 5 – x
2x – 7 + 7 > 5 – x + 7
2x > 12 – x
2x + x > 12 – x + x
3x > 12
Dividing both the sides by 3 we get,
`(3x)/3 > 12/3`
x > 4
∴ x ∈ (4, ∞) ...(1)
Then, let us consider the second inequality.
11 – 5x ≤ 1
11 – 5x – 11 ≤ 1 – 11
– 5x ≤ – 10
Dividing both the sides by 5 we get,
`(– 5x)/5 ≤ (–10)/5`
–x ≤ –2
x ≥ 2
∴ x ∈ (2, ∞) ...(2)
From (1) and (2) we get
x ∈ (4, ∞) ∩ (2, ∞)
x ∈ (4, ∞)
Hence, the solution of the given system of inequations is (4, ∞).
APPEARS IN
RELATED QUESTIONS
Solve: −4x > 30, when x ∈ R
Solve: −4x > 30, when x ∈ N
Solve: 4x − 2 < 8, when x ∈ N
3x + 9 ≥ −x + 19
\[\frac{x - 1}{3} + 4 < \frac{x - 5}{5} - 2\]
\[\frac{2x + 3}{4} - 3 < \frac{x - 4}{3} - 2\]
\[\frac{5x + 8}{4 - x} < 2\]
2x + 6 ≥ 0, 4x − 7 < 0
Solve each of the following system of equations in R.
\[\frac{7x - 1}{2} < - 3, \frac{3x + 8}{5} + 11 < 0\]
Solve
\[\left| x + \frac{1}{3} \right| > \frac{8}{3}\]
Solve \[\frac{1}{\left| x \right| - 3} < \frac{1}{2}\]
Solve
\[\left| \frac{2x - 1}{x - 1} \right| > 2\]
Solve \[\left| x - 1 \right| + \left| x - 2 \right| + \left| x - 3 \right| \geq 6\]
Solve \[\frac{\left| x - 2 \right| - 1}{\left| x - 2 \right| - 2} \leq 0\]
Solve \[\left| 3 - 4x \right| \geq 9\]
Mark the correct alternative in each of the following:
Given that x, y and b are real numbers and x\[<\]y, b\[>\]0, then
Mark the correct alternative in each of the following:
If x is a real number and \[\left| x \right|\]\[<\]5, then
Mark the correct alternative in each of the following:
If \[\left| x + 2 \right|\]\[\leq\]9, then
Mark the correct alternative in each of the following:
The linear inequality representing the solution set given in 
Mark the correct alternative in each of the following:
If \[\left| x + 3 \right|\]\[\geq\]10, then
Solve the inequality, 3x – 5 < x + 7, when x is a natural number.
The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160 cm, then ______.
If `1/(x - 2) < 0`, then x ______ 2.
If |x − 1| ≤ 2, then –1 ______ x ______ 3
If p > 0 and q < 0, then p + q ______ p.
Solve for x, the inequality given below.
`4/(x + 1) ≤ 3 ≤ 6/(x + 1)`, (x > 0)
Solve for x, the inequality given below.
|x − 1| ≤ 5, |x| ≥ 2
Solve for x, the inequality given below.
`-5 ≤ (2 - 3x)/4 ≤ 9`
A solution of 9% acid is to be diluted by adding 3% acid solution to it. The resulting mixture is to be more than 5% but less than 7% acid. If there is 460 litres of the 9% solution, how many litres of 3% solution will have to be added?
A solution is to be kept between 40°C and 45°C. What is the range of temperature in degree fahrenheit, if the conversion formula is F = `9/5` C + 32?
The longest side of a triangle is twice the shortest side and the third side is 2cm longer than the shortest side. If the perimeter of the triangle is more than 166 cm then find the minimum length of the shortest side.
If x < 5, then ______.
If x < –5 and x > 2, then x ∈ (– 5, 2)
If `2/(x + 2) > 0`, then x ______ –2.
If p > 0 and q < 0, then p – q ______ p.
