Advertisements
Advertisements
प्रश्न
Solve for x, the inequality given below.
`-5 ≤ (2 - 3x)/4 ≤ 9`
उत्तर
`-5 ≤ (2 - 3x)/4 ≤ 9`
Multiplying each term by 4, we get
⇒ –20 ≤ 2 – 3x ≤ 36
Adding –2 each term, we get
⇒ –22 ≤ –3x ≤ 34
Dividing each term by 3, we get
⇒ `-22/3` ≤ –x ≤ `34/3`
We know that,
Multiplication by –1 inverts the inequality.
So, multiplying each term by –1, we get
⇒ `(-34)/3` ≤ x ≤ `22/3`
APPEARS IN
संबंधित प्रश्न
x + 5 > 4x − 10
\[\frac{5x}{2} + \frac{3x}{4} \geq \frac{39}{4}\]
\[\frac{5 - 2x}{3} < \frac{x}{6} - 5\]
\[\frac{4 + 2x}{3} \geq \frac{x}{2} - 3\]
\[\frac{2x + 3}{5} - 2 < \frac{3\left( x - 2 \right)}{5}\]
\[\frac{3}{x - 2} < 1\]
\[\frac{5x - 6}{x + 6} < 1\]
Solve each of the following system of equations in R.
x − 2 > 0, 3x < 18
Solve each of the following system of equations in R.
2x − 3 < 7, 2x > −4
Solve each of the following system of equations in R.
3x − 1 ≥ 5, x + 2 > −1
Solve the following system of equation in R.
x + 5 > 2(x + 1), 2 − x < 3 (x + 2)
Solve each of the following system of equations in R.
2 (x − 6) < 3x − 7, 11 − 2x < 6 − x
Solve each of the following system of equations in R.
\[0 < \frac{- x}{2} < 3\]
Solve each of the following system of equations in R.
20. −5 < 2x − 3 < 5
Solve \[\frac{\left| x + 2 \right| - x}{x} < 2\]
Solve \[\frac{\left| x - 2 \right| - 1}{\left| x - 2 \right| - 2} \leq 0\]
Solve \[1 \leq \left| x - 2 \right| \leq 3\]
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 and a are real numbers such that a\[>\]0 and \\left| x \right|\]\[>\]a, then
Solve the inequality, 3x – 5 < x + 7, when x is a whole number.
The cost and revenue functions of a product are given by C(x) = 20x + 4000 and R(x) = 60x + 2000, respectively, where x is the number of items produced and sold. How many items must be sold to realise some profit?
If –x ≤ –4, then 2x ______ 8.
If |x − 1| ≤ 2, then –1 ______ x ______ 3
The water acidity in a pool is considerd normal when the average pH reading of three daily measurements is between 8.2 and 8.5. If the first two pH readings are 8.48 and 8.35, find the range of pH value for the third reading that will result in the acidity level being normal.
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?
In drilling world’s deepest hole it was found that the temperature T in degree celcius, x km below the earth’s surface was given by T = 30 + 25(x – 3), 3 ≤ x ≤ 15. At what depth will the temperature be between 155°C and 205°C?
If x > y and z < 0, then – xz ______ – yz.
If |x + 2| > 5, then x ______ – 7 or x ______ 3.
