Solve for x the inequality \( \dfrac{4}{x+1} \le 3 \le \dfrac{6}{x+1} , (x>0) \)
\( \dfrac{1}{3} \le x \le 1 \)
Solve for x the inequality \( \dfrac{|x-2|-1}{|x-2|-2} \le 0 \)
[0,1] ∪ [3,4]
Solve for x the inequality \( \dfrac{1}{|x|-3} \le \dfrac{1}{2} \)
(−∞,−5) ∪ (−3,3) ∪ [5,∞)
Solve for x the inequalities \( |x−1| \le 5 , |x| \ge 2 \)
[−4,−2] ∪ [2,6]
Solve for x the inequality \( −5 \le \dfrac{2−3x}{4} \le 9 \)
[−\dfrac{34}{3}, \dfrac{22}{3}]
Solve for x the inequalities \( 4x+3 \ge 2x+17 , 3x−5 < −2 \)
No Solution
A company manufactures cassettes. Its cost and revenue functions are \( C(x)=26000+30x \) and \( R(x)=43x \). How many cassettes must be sold for the company to realise some profit?
More than 2000.
The water acidity in a pool is considered normal when the average pH of three readings is between 8.2 and 8.5. If first two readings are 8.48 and 8.35, find the range of the third reading.
Between 7.77 and 8.77.
A solution of 9% acid is to be diluted by adding 3% acid solution to it. If mixture is to be more than 5% but less than 7% acid and there are 460 litres of 9% solution, how many litres of 3% solution are needed?
More than 230 litres but less than 920 litres.
A solution is to be kept between 40°C and 45°C. What is the range in °F? Conversion: \( F = \dfrac{9}{5}C + 32 \)
Between 104°F and 113°F
The longest side of a triangle is twice the shortest side and the third side is 2 cm longer than the shortest. If perimeter is more than 166 cm, find minimum length of shortest side.
41 cm.
The temperature at depth x km is given by \( T = 30 + 25(x−3) \). For \( 3 \le x \le 15 \), find depth at which temperature is between 155°C and 205°C.
Between 8 km and 10 km