CA Foundation · Quantitative Aptitude · Linear Inequalities
If 2 − 5x ≤ 3x + 18 for real x, which of the following is the correct solution?
The solution is x ≥ −2. Bringing like terms together gives −16 ≤ 8x, and dividing by the positive number 8 keeps the sign direction, so x ≥ −2. Testing x = 0 confirms it.
- Ax ≤ −2
- Bx ≥ −2Correct
- Cx ≥ 2
- Dx ≤ 2
Explanation
Move terms: 2 − 18 ≤ 3x + 5x, so −16 ≤ 8x. Dividing by 8 gives x ≥ −2. Check x = 0: 2 ≤ 18 is true. The option x ≤ −2 results from wrongly reversing the sign.
Did you get it right without looking?
One question tells you little. A timed set on Linear Inequalities shows your real accuracy, how long you take and where you lose marks.
More Linear Inequalities questions
- The graph of the inequality 2x + 5y ≤ 20 is drawn. Which statement about the boundary line and the solution region is correct?
- Consider the system x + y ≤ 6, x − y ≥ 2, y ≥ 0, with x and y integers. How many ordered pairs (x, y) satisfy all three conditions?
- If x > y and both x and y are positive real numbers, which of the following must be true?
- Meera scored 72 and 85 in two tests. She wants an average of at least 80 marks over three tests, with each test marked out of 100. What is t…
- A company produces toys in batches. Let x be the number of standard batches and y be the number of deluxe batches. Standard batches require …
- A jeweller has ₹50,000 to invest. She allocates amount x to gold and amount y to silver such that the investment in gold is at least ₹5,000 …