Try to solve these maths using the table method.
For example: If 1 ≤ x ≤ 3 and 2 ≤ y ≤ 4, then which of the following must be true?
a. xy ≥ 5 b. xy ≤ 12 c. xy = 12 d. xy>3 e. None of these
If you see these types of questions, then create a table like this:
| xy | 1 | 3 |
| 2 | 2 | 6 |
| 4 | 4 | 12 |
On one side, you write the ranges of x, and on the other side, you write the ranges of y. then in between cells, you multiply the values. For example: In row 1 column 2, we have 1, and in row 2 column 1, we have 2, so the value of the cell in row 2 column 2 will be 1x2 = 2. So, we then find 4 different values: 2, 4, 6, 12. So, how does it help? You can easily find out the highest and lowest value of xy without making any mistake in the fastest time. So, the smallest value of xy is 2, and the highest is 12. From that, we can say option B is the correct answer.
Tips:
1. Use this method in maths where the range of x and y is given and you are asked to determine the value or range of xy, x/y, x+y, x-y. (If the range of x+y, x-y, or x/y is asked, use the same method but then add, subtract, or divide the values instead of multiplying as we did in the above-mentioned problem.)
2. Write the ranges of x on one side and the ranges of y on the other.
3. Be careful with the signs (<, ≤).
Practice Questions
1. If x and y are both integers and x ≤ -8 and 8 > y > 3, what is the greatest possible value of x-y?
A. 0 B. -16 C. -12 D. -15 E. Cannot be determined
EXPLANATION: For greatest possible value of x-y, we need the greatest possible value of x and the smallest possible value of y. Now, greatest possible value of x = -8 And, smallest possible value of y = 4 . So, required value = -8 - 4 = -12
2. If xy < 0 and y < 0 which of the following must be positive?
A. x – y B. 2x + 3y C. x + y D. (−y−x)/x E. 2y + x^2
EXPLANATION: If xy < 0 and y < 0 then y is negative so x is positive. Again, –y is always positive. So, x – y is always positive. So, option (a) is the right answer.
3. If b < 2, and 2x - 3b= 0, which of the following must be true?
A. x > -3 B. x < 2 C. x = 3 D. x <3 E. x > 3
EXPLANATION: x-3b='0 ⇒x= 3b/2, এখন, যদি b < 2 হয়, অবশ্যই x < 3 হবে। ; [as, b/2 < 1], অর্থাৎ, Answer D
HOW TO SOLVE INEQUALITY PROBLEMS:
Other than this type of problem, you need to manually solve the other inequality problems. Don't forget to change the sign from “>” to “<”
if you multiply or divide a negative value into both of the sides.
Video on “ PRACTICE PROBLEMS OF INEQUALITY”