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Which of the following is equivalent to –13 ≤ 8 – 7x ≤ 85 ?

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Bunuel
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Which of the following is equivalent to –13 ≤ 8 – 7x ≤ 85 ? [#permalink] New post   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) \(|x – 49| ≤ 36\)





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chetan2u
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Which of the following is equivalent to 13 8 7x 85 ? [#permalink] New post   22 Feb 2022, 22:36
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Bunuel wrote:
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

\(–13 ≤ 8 – 7x ≤ 85\)

\(-(85) ≤ -(8 – 7x) ≤ -(-13)\)

\(–85 ≤ 7x-8 ≤ 13\)

\(–77 ≤ 7x ≤ 21\)

\(–11 ≤ x ≤ 3\)

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
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Re: Which of the following is equivalent to 13 8 7x 85 ? [#permalink] New post   26 Jun 2023, 05:03
chetan2u
Quote:
Simplify the inequality
–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?
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chetan2u
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Which of the following is equivalent to 13 8 7x 85 ? [#permalink] New post   26 Jun 2023, 05:30
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achloes wrote:
chetan2u
Quote:
Simplify the inequality

\(–13 ≤ 8 – 7x ≤ 85\)

\(-(85) ≤ -(8 – 7x) ≤ -(-13)\)

\(–85 ≤ 7x-8 ≤ 13\)

\(–77 ≤ 7x ≤ 21\)

\(–11 ≤ x ≤ 3\)

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?


When you multiply inequality by -, the inequality sign is changed.­
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Which of the following is equivalent to 13 8 7x 85 ? [#permalink] New post   11 Mar 2024, 02:43
chetan2u wrote:
Bunuel wrote:
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

\(–13 ≤ 8 – 7x ≤ 85\)

\(-(85) ≤ -(8 – 7x) ≤ -(-13)\)

\(–85 ≤ 7x-8 ≤ 13\)

\(–77 ≤ 7x ≤ 21\)

\(–11 ≤ x ≤ 3\)

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

­Understand that the midpoint is -4, but why does the answer become x+4? Thanks­
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Bunuel
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Which of the following is equivalent to 13 8 7x 85 ? [#permalink] New post   11 Mar 2024, 02:53
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patriciachr wrote:
chetan2u wrote:
Bunuel wrote:
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

\(–13 ≤ 8 – 7x ≤ 85\)

\(-(85) ≤ -(8 – 7x) ≤ -(-13)\)

\(–85 ≤ 7x-8 ≤ 13\)

\(–77 ≤ 7x ≤ 21\)

\(–11 ≤ x ≤ 3\)

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

­Understand that the midpoint is -4, but why does the answer become x+4? Thanks­

­
\(–13 ≤ 8 – 7x ≤ 85\) is equivalent to \(–11 ≤ x ≤ 3\).

Similarly, option A, \(|x + 4| ≤ 7\), is equivalent to the same expression: 

\(-7 ≤ x + 4 ≤ 7\)

\(-11 ≤ x ≤ 2\)

 ­
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Which of the following is equivalent to 13 8 7x 85 ? [#permalink]
11 Mar 2024, 02:53
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