Advertisements
Advertisements
Question
If x ∈ Z, solve 2 + 4x < 2x – 5 ≤ 3x. Also represent its solution on the number line.
Solution
2 + 4x < 2x – 5 ≤ 3x
2 + 4x < 2x – 5 and 2x – 5 ≤ 3x => 4x – 2x < – 5 – 2 ,and 2x – 3x ≤ 5
⇒ 2x < - 7 and - x ≤ 5
⇒ `x < -(7)/(2)` and x ≥ - 5 and - 5 ≤ x
∴ - 5 ≤ x < - `(7)/(2)`
∵ x ∈ Z
∴ Solution set = {-5, -4}
Solution set on Number line
APPEARS IN
RELATED QUESTIONS
Solve the following inequation, write the solution set and represent it on the number line.
`-3(x - 7) >= 15 - 7x > (x+1)/3`, x ∉ R
Find the values of x, which satisfy the inequation `-2 5/6 < 1/2 - (2x)/3 ≤ 2, x ∈ W`. Graph the solution set on the number line.
For the following inequations, graph the solution set on the real number line:
– 4 ≤ 3x – 1 < 8
Represent the solution of the following inequalities on the real number line:
7 – x ≤ 2 – 6x
The diagram represents two inequations A and B on real number lines:
- Write down A and B in set builder notation.
- Represent A ∪ B and A ∩ B' on two different number lines.
Solve the following in equation and write the solution set:
13x – 5 < 15x + 4 < 7x + 12, x ∈ R
Solve the following linear in-equation and graph the solution set on a real number line:
2x - 11≤ 7 - 3x, x ∈ N
Solve the following linear in-equation and graph the solution set on a real number line:
2(3x-5) > 5(13-2x), x ∈ W
If x ∈ R (real numbers) and – 1 < 3 – 2x ≤ 7, find solution set and represent it on a number line.
Solve the following inequation, write the solution set and represent it on the real number line.
`5x - 21 < (5x)/7 - 6 ≤ -3 3/7 + x, x ∈ R`
