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 product was initially priced at 200. During a sale, the price was first decreased by 20%. Later, due to high demand, the sale price was further increa...
What will be the fraction of 20%
Ajay spent 30% of his monthly income on rent and 44% of the remaining on food and the rest amount is saved by him which is Rs. 2548, then find the month...
Two students appeared in an exam and one secured 12 marks more than the other. If marks of student who got more marks is 55% of the sum of the marks of ...
A and B together have total of Rs.6000 out of which they donated 20% to the orphanage school. The remaining amount is to be then redistributed between t...
A no. is multiplied by 35 instead of being multiplied by 53. What % is the result of the required correct value?
Income of A is twice the income of B. B and A spend 75% and 85% respectively of their incomes. Find the savings of A, if B saves Rs. 18000 in a month.
A company allowed 16% commission on the total sales made by the salesman and a bonus of 1% on the sales over Rs.25000. If the salesman deposited Rs. 66...
In a train, 45% of the passengers are females. Out of total number of passengers, 65% have unreserved tickets out of which 27% are females. How much per...
In a town of 5000 inhabitants, 75% are males, and 20% of them are literate. If 25% of the total population is literate, what percentage of the female po...
