Advertisements
Advertisements
Question
If |x − 1| ≤ 2, then –1 ______ x ______ 3
Solution
If |x − 1| ≤ 2, then –1 ≤ x ≤ 3.
Explanation:
|x − 1| ≤ 2 ⇒ –2 ≤ x – 1 ≤ 2 ⇒ –1 ≤ x ≤ 3.
APPEARS IN
RELATED QUESTIONS
Solve: −4x > 30, when x ∈ Z
x + 5 > 4x − 10
\[2\left( 3 - x \right) \geq \frac{x}{5} + 4\]
−(x − 3) + 4 < 5 − 2x
\[\frac{4 + 2x}{3} \geq \frac{x}{2} - 3\]
\[\frac{5x + 8}{4 - x} < 2\]
Solve each of the following system of equations in R.
2x − 7 > 5 − x, 11 − 5x ≤ 1
2x + 6 ≥ 0, 4x − 7 < 0
Solve each of the following system of equations in R.
11 − 5x > −4, 4x + 13 ≤ −11
Solve each of the following system of equations in R.
2 (x − 6) < 3x − 7, 11 − 2x < 6 − x
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.
10 ≤ −5 (x − 2) < 20
Solve \[\frac{\left| x - 2 \right|}{x - 2} > 0\]
Solve \[\frac{1}{\left| x \right| - 3} < \frac{1}{2}\]
Solve \[\frac{\left| x - 2 \right| - 1}{\left| x - 2 \right| - 2} \leq 0\]
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
Solve the inequality, 3x – 5 < x + 7, when x is an integer.
Solve for x, |x + 1| + |x| > 3.
If –x ≤ –4, then 2x ______ 8.
Solve for x, the inequality given below.
`4/(x + 1) ≤ 3 ≤ 6/(x + 1)`, (x > 0)
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 –3x + 17 < –13, then ______.
If x is a real number and |x| < 3, then ______.
If x > – 5, then 4x ______ –20.
If |x + 2| > 5, then x ______ – 7 or x ______ 3.
