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22 Feb 2022, 07:00
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Which of the following is equivalent to \(–13 ≤ 8 – 7x ≤ 85\)?
(A) \(|x + 4| ≤ 7\)
(B) \(|x – 4| ≤ 7\)
(C) \(|x + 11| ≥ –3\)
(D) \(|x – 36| ≤ 49\)
(E) \(|x – 49| ≤ 36\)
Are You Up For the Challenge: 700 Level Questions
(A) \(|x + 4| ≤ 7\)
(B) \(|x – 4| ≤ 7\)
(C) \(|x + 11| ≥ –3\)
(D) \(|x – 36| ≤ 49\)
(E) \(|x – 49| ≤ 36\)
Are You Up For the Challenge: 700 Level Questions
22 Feb 2022, 22:36
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Bunuel
Which of the following is equivalent to \(–13 ≤ 8 – 7x ≤ 85\)?
(A) \(|x + 4| ≤ 7\)
(B) \(|x – 4| ≤ 7\)
(C) \(|x + 11| ≥ –3\)
(D) \(|x – 36| ≤ 49\)
(E) \(|x – 49| ≤ 36\)
Simplify the inequality(A) \(|x + 4| ≤ 7\)
(B) \(|x – 4| ≤ 7\)
(C) \(|x + 11| ≥ –3\)
(D) \(|x – 36| ≤ 49\)
(E) \(|x – 49| ≤ 36\)
\(–13 ≤ 8 – 7x ≤ 85\)
\(-(85) ≤ -(8 – 7x) ≤ -(-13)\)
\(–85 ≤ 7x-8 ≤ 13\)
\(–77 ≤ 7x ≤ 21\)
\(–11 ≤ x ≤ 3\)
Now, all options are of the type \(|x - a| ≤ b\), which is a-b ≤ x ≤ a+b
We can write \(–11 ≤ x ≤ 3\) as \(–4-7 ≤ x ≤ -4+7\). Thus, a=-4 and b=7
\(|x - a| ≤ b\) => \(|x -(-4)| ≤ 7\) => \(|x +4)| ≤ 7\)
A
OR
After simplifying to \(–11 ≤ x ≤ 3\), we can also open the MOD in each option to get the answer.
(A) \(|x + 4| ≤ 7\)
\(x + 4 ≤ 7........x\leq 3\)
\(-(x + 4 ≤ 7)........x\geq -11\)
Exactly what we are looking for.
A
26 Jun 2023, 05:03
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chetan2u
When simplifying, why do you flip the extreme values of the inequality?
I got 3≤ x ≤ -11 after simplification, which I then broke down to x ≤ -11 or x ≥ 3.
What am I doing wrong?
Quote:
Simplify the inequality
–13≤8–7x≤85.................−(85)≤−(8–7x)≤−(−13)...........–85≤7x−8≤13...........–77≤7x≤21...........–11≤x≤3
–13≤8–7x≤85.................−(85)≤−(8–7x)≤−(−13)...........–85≤7x−8≤13...........–77≤7x≤21...........–11≤x≤3
When simplifying, why do you flip the extreme values of the inequality?
I got 3≤ x ≤ -11 after simplification, which I then broke down to x ≤ -11 or x ≥ 3.
What am I doing wrong?
