CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Inequalities Involving Modulus Function

Number of int...

Question

Number of integer values of $x$ satisfying the inequality
$| x - 3 | + | 2 x + 4 | + | x | \leq 11$ is

Open in App

Solution

$| x - 3 | + | 2 x + 4 | + | x | \leq 11$
If $x \geq 3$ ,
$x - 3 + 2 x + 4 + x \leq 11$
$\Rightarrow 4 x \leq 10$
$\Rightarrow x \leq 2.5$ No solution

If $0 \leq x < 3$ ,
$- x + 3 + 2 x + 4 + x \leq 11 \Rightarrow x \leq 2 \Rightarrow x \in [0, 2]$

If $- 2 \leq x < 0$ ,
$- x + 3 + 2 x + 4 - x \leq 11$
$\Rightarrow 7 \leq 11$ which is true
$\Rightarrow x \in [- 2, 0)$

If $x < - 2$ ,
$- x + 3 - 2 x - 4 - x \leq 11$
$\Rightarrow - 4 x - 1 \leq 11$
$\Rightarrow x \geq - 3 \Rightarrow x \in [- 3, - 2)$

Hence, $x \in [0, 2] \cup [- 2, 0) \cup [- 3, - 2)$
i.e., $x \in [- 3, 2]$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Number of integer values of

x

satisfying the inequality

| x - 3 | + | 2 x + 4 | + | x | \leq 11

Q. The values of

x

satisfying the inequality

{[{tan}^{- 1} x]}^{2} - [{tan}^{- 1} x] - 2 \leq 0

where [ ] denote integer part, is

Q. Number of integers

\leq 10

satisfying the inequality

2 {log}_{1 / 2} (x - 1) \leq \frac{1}{3} - \frac{1}{{log}_{x^{2} - x} 8}

Q. What are the integer values of x which satisfy the inequalities

x > - 2

x \leq 2

?

Q. The minimum value of x satisfying the inequality

4^{- x + 0.5} - 7 \cdot 2^{- x} \leq 4

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Inequalities Involving Modulus Function

Standard XIII Mathematics

Join BYJU'S Learning Program

CrossIcon