Question

If 8 times an integer x is increased by 5, the result is always less than 36 and greater than 22. Form an inequality and solve it to find the greatest possible value of
x

Answer 1

Answer:

3

Step-by-step explanation:

8 times of x, increased by 5 is 8x + 5.

 According to question :

   8x + 5 is always less then 36 and greater than 22.

It means, 8x + 5 < 36  as well as 8x + 5 > 22

Equality formed : 22 < 8x + 5 < 36

⇒ 22 < 8x + 5      &  8x + 5 , 36

⇒ 22 - 5  < 8x     & 8x < 36 - 5

⇒ 17 < 8x         &  8x < 31

⇒ 17/8 < x       & x < 31/8

⇒ 2.125 < x    &  x < 3.874

⇒ 2,125 < x < 3.875

  Hence,

x( being an integer ) can be 3 .

 Hence the only possible value of x is 3

Answer 2

Answer:

Given : If 8 times an integer x is increased by 5, the result is always less than 36 and greater than 22.

$\rule{100}{0.8}$

$\underline{\bigstar\:\sf{According\:to\:the\:Question :}}$

$:\implies\sf 36 > (8 \times Number+5) > 22\\\\\\:\implies\sf 36 > (8x + 5) > 22\\\\\\:\implies\sf 36 > (8x + 5)\qquad\&\qquad(8x + 5) > 22\\\\\\:\implies\sf 36 - 5 > 8x\qquad\&\qquad8x > 22 - 5\\\\\\:\implies\sf 31 > 8x\qquad\&\qquad8x > 17\\\\\\:\implies\sf \dfrac{31}{8} > x\qquad\&\qquad x > \dfrac{17}{8}\\\\\\:\implies\underline{\boxed{\sf 3.87 \:> \:x \:> \:2.12}}$

• As It's an Integer and Falls between 3.87 and 2.12

⠀

$\therefore\:\underline{\textsf{Hence, greatest possible value of x is \textbf{3}}}.$