Question
Solve for x: |2x − 5| + |x + 1| ≤
10.Solution
ATQ,
Critical points at x = 2.5 and x = −1. Case 1: x ≥ 2.5 ⇒ (2x − 5) + (x + 1) ≤ 10 ⇒ 3x − 4 ≤ 10 ⇒ x ≤ 14/3. So 2.5 ≤ x ≤ 14/3. Case 2: −1 ≤ x ≤ 2.5 ⇒ (5 − 2x) + (x + 1) ≤ 10 ⇒ 6 − x ≤ 10 ⇒ −x ≤ 4 ⇒ x ≥ −4. In this band, it’s all valid: −1 ≤ x ≤ 2.5. Case 3: x ≤ −1 ⇒ (5 − 2x) + (−x − 1) ≤ 10 ⇒ 4 − 3x ≤ 10 ⇒ −3x ≤ 6 ⇒ x ≥ −2. So in this band: −2 ≤ x ≤ −1. Combine: −2 ≤ x ≤ 14/3. Answer: x ∈ [−2, 14/3].
A solution contains petrol and kerosene in a ratio of 3:5. 16 liters of the solution is replaced with petrol to make a ratio of 5:3. Find the original a...
In what ratio coffee at 265 Rs/kg should be mixed with the coffee at 305 Rs/kg so that after mixture its rate become 280 Rs/kg if the quantity of 1st ty...
In a Mixture, the ratio of Milk and Water is 7: 5. If 12 litre mixture drawn off and replace by 8 litre water then the ratio of Milk and Water become 1...
A sum of ₹4,360 was to be divided among A, B, C, and D in the ratio 3:4:5:8, but it was divided in the ratio 1/3:1/4:1/5:1/8. Was divided by mistake: ...
2Kg of sugar at Rs 20 per Kg is mixed with 3 Kg of 2nd type of sugar to get a mixture costing Rs 35 per Kg. Find the price of the costlier sugar ?
Cost of two types of pulses is Rs.25 and Rs, 30 per kg, respectively. If both the pulses are mixed together in the ratio 2:3, then what should be the pr...
The average of n numbers is 60. If each of 55% of the numbers is increased by 12 and each of the remaining numbers is decreased by 12, then the new aver...
Find the smallest number which when successively divided by 4, 7 and 5 will give the remainder 2, 1, 3.
Simplify the following expression:
The Jar contains only 8 litres of milk and the rest is water. A new mixture in which concentration of milk is 30%, is to be formed by replacing the Jar ...
