Algebra

Inequalities

Medium

Find the sum of the smallest value and the greatest value of $x$ that satisfy the inequality $|5x + 5| - 8 \leq 17$ .

-2

-4

✅ Correct Option: 2

$|5x + 5| - 8 \leq 17$

$|5x + 5| \leq 25$

$5|x + 1| \leq 25$

$|x + 1| \leq 5$

$|y| \leq 5$ means $y$ lies between $-5$ and $5$ :

$-5 \leq x + 1 \leq 5$

$-6 \leq x \leq 4$

Smallest value of $x = -6$

Greatest value of $x = 4$

Sum $= -6 + 4 = -2$

Therefore, the required sum is $-2$ .

2024: Slot 2

A pair of consecutive odd positive integers, both of which are smaller than 19, have a sum that is more than 22. How many such pairs will be there, if we allow a number to be in more than one pair?

BBA-DBE Bangalore 2026

A company produces rectangular advertising boards such that the width is always at least 8 cm shorter than the length, and both the length and width are integers. If the area of a board cannot be more than $320\text{ cm}^2$ and the width is $x$ cm, then find the maximum possible value of $x$ .

Find the sum of the smallest value and the greatest value of xxx that satisfy the inequality ∣5x+5∣−8≤17|5x + 5| - 8 \leq 17∣5x+5∣−8≤17.

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BBA-DBE Bangalore Past Year Questions (Topic-Wise)

Find the sum of the smallest value and the greatest value of $x$ that satisfy the inequality $|5x + 5| - 8 \leq 17$ .