Advertisements
Advertisements
Question
Mark the correct alternative in each of the following:
If x is a real number and \[\left| x \right|\]\[<\]5, then
Options
(a) x\[\geq\]5
(b) \[-\]5\[<\]x\[<\]5
(c) x\[\leq\]\[-\]5
(d) \[-\]5\[\leq\]x\[\leq\]5
Solution
If x is a real number.
\[\left| x \right|\]\[<\]5
⇒\[-\]5\[<\]x\[<\]5
Hence, the correct option is (b).
APPEARS IN
RELATED QUESTIONS
Solve: 12x < 50, when x ∈ N
Solve: −4x > 30, when x ∈ R
Solve: −4x > 30, when x ∈ Z
Solve: 4x − 2 < 8, when x ∈ R
Solve: 4x − 2 < 8, when x ∈ Z
Solve: 4x − 2 < 8, when x ∈ N
x + 5 > 4x − 10
\[\frac{x}{5} < \frac{3x - 2}{4} - \frac{5x - 3}{5}\]
\[\frac{2\left( x - 1 \right)}{5} \leq \frac{3\left( 2 + x \right)}{7}\]
\[\frac{5 - 2x}{3} < \frac{x}{6} - 5\]
\[\frac{4 + 2x}{3} \geq \frac{x}{2} - 3\]
\[\frac{5x + 8}{4 - x} < 2\]
\[\frac{x}{x - 5} > \frac{1}{2}\]
Solve each of the following system of equations in R.
x − 2 > 0, 3x < 18
Solve each of the following system of equations in R.
5x − 1 < 24, 5x + 1 > −24
Solve each of the following system of equations in R.
\[\frac{2x - 3}{4} - 2 \geq \frac{4x}{3} - 6, 2\left( 2x + 3 \right) < 6\left( x - 2 \right) + 10\]
Solve the following system of equation in R.
\[\frac{2x + 1}{7x - 1} > 5, \frac{x + 7}{x - 8} > 2\]
Solve each of the following system of equations in R.
20. −5 < 2x − 3 < 5
Solve
\[\left| 4 - x \right| + 1 < 3\]
Solve \[\frac{\left| x - 2 \right|}{x - 2} > 0\]
Solve \[\frac{1}{\left| x \right| - 3} < \frac{1}{2}\]
Solve \[\frac{1}{\left| x \right| - 3} \leq \frac{1}{2}\]
Solve \[1 \leq \left| x - 2 \right| \leq 3\]
Solve \[\left| 3 - 4x \right| \geq 9\]
Mark the correct alternative in each of the following:
The inequality representing the following graph is
Mark the correct alternative in each of the following:
The linear inequality representing the solution set given in 
Solve 1 ≤ |x – 2| ≤ 3.
Solve for x, |x + 1| + |x| > 3.
If x ≥ –3, then x + 5 ______ 2.
If a < b and c < 0, then `a/c` ______ `b/c`.
Solve for x, the inequality given below.
`-5 ≤ (2 - 3x)/4 ≤ 9`
The longest side of a triangle is twice the shortest side and the third side is 2cm longer than the shortest side. If the perimeter of the triangle is more than 166 cm then find the minimum length of the shortest side.
In drilling world’s deepest hole it was found that the temperature T in degree celcius, x km below the earth’s surface was given by T = 30 + 25(x – 3), 3 ≤ x ≤ 15. At what depth will the temperature be between 155°C and 205°C?
If x < –5 and x > 2, then x ∈ (– 5, 2)
If – 4x ≥ 12, then x ______ – 3.
