Advertisements
Advertisements
Question
Find the values of x which satisfy the inequation:
`-2 <= 1/2 - (2x)/3 ≤ 1 5/6; x ∈ N`
Graph the solution on the number line.
Solution
`-2 <= 1/2 - (2x)/3 ≤ 1 5/6`
`-2 <= 1/2 - (2x)/3 ` and `1/2 - (2x)/3 ≤ 1 5/6`
`-2 <= 1/2 - (2x)/3 ` and `1/2 - (2x)/3 ≤ 11/6`
`-2 <=(3-4x)/6 and (2x)/3 ≤ 11/6 - 1/2`
`-12 <=3-4x and -(2x)/3 ≤ 8/6`
– 4x ≤ 3 + 12 and – 2x ≤ – 4
`x <= 15/4 and x >= 4/(-2)`
x ≤ 3.75 and x ≥ – 2
Thus, the solution set is {x ∊ N: – 2 ≤ x ≤ 3.75}
Since x ∊ N, the values of x are 1, 2, 3
The solution on number line is given by
APPEARS IN
RELATED QUESTIONS
If the replacement set is the set of whole numbers, solve:
`7 - 3x >= - 1/2`
If the replacement set is the set of whole numbers, solve:
`x - 3/2 < 3/2 - x`
Represent the solution of the following inequalities on the real number line:
1 + x ≥ 5x – 11
x ∈ {real numbers} and –1 < 3 – 2x ≤ 7, evaluate x and represent it on a number line.
Solve and graph the solution set of:
5 > p – 1 > 2 or 7 ≤ 2p – 1 ≤ 17, p ∈ R
Solve for x in the following in-equation, if the replacement set is R;
3x + 25 < 8x - 10
Find the solution set of the following inequalities and draw the graph of their solutions sets:
| x - 1 | > 3
Given 20 – 5 x < 5 (x + 8), find the smallest value of x, when
(i) x ∈ I
(ii) x ∈ W
(iii) x ∈ N.
Find three smallest consecutive natural numbers such that the difference between one-third of the largest and one-fifth of the smallest is at least 3
The minimum value of x for the inequation 5x – 4 ≥ 18 – 6x is ______.
