4 Views

Question : If $4(x+5)-3>6-4x\geq x-5$, then the value of $x$ is:

Option 1: –2

Option 2: –1

Option 3: 3

Option 4: 4


Team Careers360 20th Jan, 2024
Answer (1)
Team Careers360 23rd Jan, 2024

Correct Answer: –1


Solution : To solve the compound inequality $4(x+5)–3 > 6 –4x \geq x – 5$
Solving each inequality one by one,
$4(x+5) - 3 > 6- 4x$
$⇒4x + 20 -3 > 6 - 4x$
$⇒4x + 17 > 6- 4x$
$⇒8x + 17 > 6$
$⇒x > \frac{–11}{8}$
So, the solution to the first inequality is $x > \frac{–11}{8}$.
Also, \(6 -4x \geq x - 5\)
$⇒6 \geq 5x -5$
$⇒11 \geq 5x$
$⇒\frac{11}{5} \geq x$
So, the values of $x$ that satisfy the original compound inequality are in the range: $\frac{–11}{8} < x \leq \frac{11}{5} = –1.375 < x \leq 2.2$
So, the value of $x$ is –1.
Hence, the correct answer is –1.

How to crack SSC CHSL

Candidates can download this e-book to give a boost to thier preparation.

Download Now

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books