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Find the pairs of consecutive even positive integers both of which should be less than 12 and not 10
Let x be the smaller of the two consecutive even positive integers, then the other even integer is x + 2.
Given x < 10 and x + (x + 2) > 11.
⇒ x < 10, and 2x + 2 > 11.
⇒ x < 10, 2x > 9
⇒ x < 10, x > 9/2
⇒ 10 < x > 9/2
∴ the required parity even integers is (6, 8)
Which of the following is not a linear inequality?
Quadratic inequalities can be of the following forms:
ax^{2 }+ bx + c > 0
ax^{2 }+ bx + c ≥ 0
ax^{2 }+ bx + c < 0
ax^{2 }+ bx + c ≤ 0
For a student to qualify for a certain course, the average of his marks in the permitted 3 attempts must be more than 60. His first two attempts yielded only 45 and 62 marks respectively. What is the minimum score required in the third attempt to qualify?
Let marks required be x
= (45 + 62 + x)/3 = 60
45+62+ x = 60*3
107 + x = 180
x = 180  107
x = 73
Which one of them is the solution for x, when x is integer and 12 x > 30?
when x=3
the 12(3) = 36 which is greater than 30
Find the value of x which satisfies 5x – 3 < 7, where x is a natural number.
The given inequality is 5x– 3 < 7
=> 5x – 3 + 3 < 7 + 3 [3 is added both sides]
=> 5x < 10
=> x < 10/5
=> x < 2
When x is a real number, the solutions of the given inequality are given by x < 2, i.e., all real numbers x which are less than 2.
5x + 2 < 7x  4
2 + 4 < 7x + 5x
6 < 12x
x > 1/2
The solution to 5x3<3x+1, when x is an integer, is
We have 5x−3<3x+1
⇒ 5x − 3 + 3 < 3x + 1 + 3
⇒ 5x < 3x + 4
⇒ 5x − 3 × < 3x + 4 − 3x
⇒ 2x < 4 ⇒ x < 2
When x is an integer the solutions of the given inequality are {.............,−4,−3,−2,−1,0,1}
By solving inequality 3(a  6) < 4 + a, answer will be
A point P lies in the solution region of 3x – 7 > x + 3. So the possible coordinates of P are
3x  7> x + 3
2 x > 10
x > 5
so x coordinate should be > 5
5x + 6 < 2x  3
5x  2x <  3 6
⇒ 3x < 9
x < 3
As we move to right side on the number line the value increases. i.e. To the right of the point (3,0)
The solution of inequality 4x + 3 < 5x + 7 when x is a real number is
4x + 3 < 5x + 7
subtract 4 both sides,
4x + 3  3 < 5x + 7  3
⇒ 4x < 5x + 4
subtract ' 5x ' both sides ,
[ equal number may be subtracted from both sides of an inequality without affecting the sign of inequality]
4x  5x < 5x + 4  5
x < 4
now, multiple with (1) then, sign of inequality change .
x.(1) > 4(1)
x > 4
hence, x€ ( 4 , ∞)
Two less than 5 times a number is greater than the third multiple of the number. So the number must be
Two less than 5 times a number is greater than the third multiple of the number.
5x  2 >3x
5x  3x > 2
2x > 2
x > 1
By solving the inequality 6x  7 > 5, the answer will be
Find the value of x when x is a natural number and 24x< 100.
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