Linear Inequalities

The solution set for the inequality $|x + 1| + |x - 1| + |x - 3| \geq 9$ is:
1. $(- 1, 1) \cup (3, \infty)$
2. $(- \infty, - 1) \cup (1, 3)$
3. $(- \infty, - 1] \cup [3, \infty)$
4. $(- \infty, - 2] \cup [4, \infty)$
$2 x - 3 \geq 3 x + 5$ can be represented as:
1. $x \geq - 8$
2. $x \leq - 8$
3. $x \geq 8$
4. $x \leq 8$
Point satisfying the inequation 3x + 4y < 11 is:
1. (2, 4)
2. (- 1, 0)
3. (1, 6)
4. (1, 3)
Mohan has Rs. 500 and Sohan has Rs. 600. Mohan wants to buy two similar pens and Sohan wants to buy three pens of the same type. With the remaining amount with them, they wish to buy a chess board. If x represents the price of a pen and y represents the price of a chess board, an expression using inequalities, to ascertain the maximum price possible for a pen and a chess board is:
1. $2 x \leq 500, 3 x \leq 600, y \leq 1100$
2. $5 x \leq 1100, y \leq 1100$
3. $2 x \leq 500, 3 x \leq 600, 5 x + y \leq 1100$
4. $2 x \leq 500, 3 x \leq 600, y \leq 100$
If 4 is added to three times a positive integer, then it is greater than four times that positive integer reduced by 1. The solution set is:
1. {1, 2, 3, 4, 5, 6}
2. {1, 2, 3}
3. {1, 2, 3, 4, 5}
4. {1, 2, 3, 4}
If $2 \leq \frac{4 x^{2} - 9 x + 20}{x^{2} + 2} \leq 3$ , $x \in R$ , then x is:
1. $(- \infty, 2] \cup [7, \infty)$
2. $(- \infty, 2) \cup (7, \infty)$
3. $[2, 7]$
4. $(2, 7)$
The solution set of $||x + 1| - 2| \leq 4$ , where $x \in R$ is:
1. $x \in [1, 5]$
2. $x \in [- 3, 1]$
3. $x \in [- 3, 7)$
4. $x \in [- 7, 5]$
x is an integer; one-third of the next integer is greater than one-fourth of its previous integer by 2. The minimum value of x is:
1. 18
2. 15
3. 17
4. 16
Solve for $x \in R$ , where $3^{x} + 3^{1 - x} - 4 < 0$ .
1. x < 1
2. 1 < x < 3
3. 0 < x < 1
4. - 1 < x < 1
The solution set in R for the inequality ${(x + 2)}^{5} - {(x - 4)}^{5} \leq 3126$ is:
1. $x \in (- 2, 4)$
2. $x \in [- 1, 3]$
3. $x \in (- \infty, 3]$
4. $x \in [- 1, \infty)$
If x < 5, then:
1. - x < - 5
2. $- x \leq - 5$
3. - x > - 5
4. $- x \geq - 5$
Given that x, y and b are real numbers and x < y, b < 0, then:
1. $\frac{x}{b} < \frac{y}{b}$
2. $\frac{x}{b} \leq \frac{y}{b}$
3. $\frac{x}{b} > \frac{y}{b}$
4. $\frac{x}{b} \geq \frac{y}{b}$
If $- 3 x + 17 < - 13$ , then:
1. $x \in (10, \infty)$
2. $x \in [10, \infty)$
3. $x \in (- \infty, 10]$
4. $x \in [- 10, 10)$
If x is a real number and $|x| < 3$ , then:
1. $x \geq 3$
2. $- 3 < x < 3$
3. $x \leq - 3$
4. $- 3 \leq x \leq 3$
x and b are real numbers. If b > 0 and $|x| > b$ , then:
1. $x \in (- b, \infty)$
2. $x \in (- \infty, b)$
3. $x \in (- b, b)$
4. $x \in (- \infty, - b) \cup (b, \infty)$
If $|x - 1| > 5$ , then:
1. $x \in (- 4, 6)$
2. $x \in [- 4, 6]$
3. $x \in [- \infty, - 4) \cup (6, \infty)$
4. $x \in [- \infty, - 4) \cup [6, \infty)$
If $|x + 2| \leq 9$ , then:
1. $x \in (- 7, 11)$
2. $x \in [- 11, 7]$
3. $x \in (- \infty, - 7) \cup (11, \infty)$
4. $x \in (- \infty, - 7) \cup [11, \infty)$
The inequality representing the following graph is:
1. $|x| < 5$
2. $|x| \leq 5$
3. $|x| > 5$
4. $|x| \geq 5$
Choose the correct value of x represented on a number line:
1. $x \in (- \infty, 5)$
2. $x \in (- \infty, 5]$
3. $x \in [5, \infty)$
4. $x \in (5, \infty)$
Choose the correct value of x represented on a number line:
1. $x \in (\frac{9}{2}, \infty)$
2. $x \in [\frac{9}{2}, \infty)$
3. $x \in [- \infty, \frac{9}{2})$
4. $x \in (- \infty, \frac{9}{2}]$
Choose the correct value of x represented on a number line:
1. $x \in (- \infty, \frac{7}{2})$
2. $x \in (- \infty, \frac{7}{2}]$
3. $x \in [\frac{7}{2}, - \infty)$
4. $x \in (\frac{7}{2}, \infty)$
Choose the correct value of x represented on a number line:
1. $x \in (- \infty, - 2)$
2. $x \in (- \infty, - 2]$
3. $x \in (- 2, \infty)$
4. $x \in [- 2, \infty)$
Given that x, y and b are real numbers and x < y, b > 0, then:
1. $\frac{x}{b} < \frac{y}{b}$
2. $\frac{x}{b} \leq \frac{y}{b}$
3. $\frac{x}{b} > \frac{y}{b}$
4. $\frac{x}{b} \geq \frac{y}{b}$
If x and a are real numbers such that a > 0 and $|x| > a$ , then:
1. $x \in (- a, \infty)$
2. $x \in [- \infty, a]$
3. $x \in (- a, a)$
4. $x \in (- \infty, - a) \cup (a, \infty)$
The solution set of the inequation $|x + 2| \leq 5$ is:
1. (- 7, 5)
2. [- 7, 3]
3. [- 5, 5]
4. (- 7, 3)
If $\frac{|x - 2|}{x - 2} \geq 0$ , then:
1. $x \in [2, \infty)$
2. $x \in (2, \infty)$
3. $x \in (- \infty, 2)$
4. $x \in (- \infty, 2]$
If $|x + 3| \geq 1$ , then:
1. $x \in (- 13, 7]$
2. $x \in (- 13, 7)$
3. $x \in (- \infty, - 13) \cup (7, \infty)$
4. $x \in (- \infty, - 13] \cup [7, \infty)$
A solution is to be kept between $30 ° C$ and $35 ° C$ . What is the range of temperature in degree Fahrenheit.What is the range of temperature in degree Fahrenheit if conversion formula is given by $C = \frac{5}{9} (F - 32)$ where C and F represent temperature in degree Celcius and degree Fahrenheit?
1. Between $40 ° F$ and $60 ° F$
2. Between $86 ° F$ and $95 ° F$
3. Between $30 ° F$ and $35 ° F$
4. Between $76 ° F$ and $105 ° F$
The marks scored by Rohit in two tests were 65 and 70. Find the minimum marks he should score in the third test to have an average of atleast 65 marks.
1. 60
2. 65
3. 70
4. 75
A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and third length is to be twice as long as the shortest. What are the possible lengths for the shortest board if the third piece is to be at least 5 cm longer than the second?
1. $3 \leq x \leq 91$
2. $8 \leq x \leq 22$
3. $5 \leq x \leq 91$
4. $3 \leq x \leq 5$

Linear Inequalities

Quiz