Advertisements
Advertisements
प्रश्न
Solve 1 ≤ |x – 2| ≤ 3.
उत्तर
We have 1 ≤ |x – 2| ≤ 3
⇒ |x − 2| ≥ 1 and |x – 2| ≤ 3
⇒ (x – 2 ≤ –1 or x – 2 ≥ 1) and (–3 ≤ x – 2 ≤ 3)
⇒ (x ≤ 1 or x ≥ 3) and (–1 ≤ x ≤ 5)
⇒ x ∈ `(-oo, 1]` ∪ `[3, oo)` and x ∈ [–1, 5]
Combining the solutions of two inequalities, We have x ∈ [–1, 1] ∪ [3, 5].
APPEARS IN
संबंधित प्रश्न
Solve: −4x > 30, when x ∈ Z
Solve: 4x − 2 < 8, when x ∈ Z
3x − 7 > x + 1
−(x − 3) + 4 < 5 − 2x
\[\frac{5x}{2} + \frac{3x}{4} \geq \frac{39}{4}\]
\[\frac{6x - 5}{4x + 1} < 0\]
\[\frac{4x + 3}{2x - 5} < 6\]
\[\frac{5x + 8}{4 - x} < 2\]
\[\frac{x - 1}{x + 3} > 2\]
Solve each of the following system of equations in R.
2x − 7 > 5 − x, 11 − 5x ≤ 1
Solve each of the following system of equations in R.
2x + 5 ≤ 0, x − 3 ≤ 0
Solve each of the following system of equations in R.
3x − 1 ≥ 5, x + 2 > −1
Solve each of the following system of equations in R.
4x − 1 ≤ 0, 3 − 4x < 0
Solve each of the following system of equations in R.
10 ≤ −5 (x − 2) < 20
Solve
\[\left| x + \frac{1}{3} \right| > \frac{8}{3}\]
Solve
\[\left| \frac{3x - 4}{2} \right| \leq \frac{5}{12}\]
Solve \[\frac{1}{\left| x \right| - 3} \leq \frac{1}{2}\]
Mark the correct alternative in each of the following:
If − 3x\[+\]17\[< -\]13, then
Mark the correct alternative in each of the following:
If x and a are real numbers such that a\[>\]0 and \\left| x \right|\]\[>\]a, then
Mark the correct alternative in each of the following:
\[\left| x - 1 \right|\]\[>\]5, then
Solve the inequality, 3x – 5 < x + 7, when x is a whole number.
Solve |3 – 4x| ≥ 9.
Solve for x, the inequality given below.
`(|x - 2| - 1)/(|x - 2| - 2) ≤ 0`
A company manufactures cassettes. Its cost and revenue functions are C(x) = 26,000 + 30x and R(x) = 43x, respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realise some profit?
x and b are real numbers. If b > 0 and |x| > b, then ______.
If – 4x ≥ 12, then x ______ – 3.
If `2/(x + 2) > 0`, then x ______ –2.
If x > – 5, then 4x ______ –20.
