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Which of the following numbers satisfies the absolute value inequality
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11 Feb 2022, 08:30
11 Feb 2022, 08:30
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Which of the following numbers satisfies the absolute value inequality shown?
\(|2x-1|>5\)
Indicate all such numbers
A. \(- \pi\)
B. \(- \frac{3}{2}
\)
C. \(- \sqrt{10}
\)
D. \(\frac{\sqrt{2}}{2}\)
E. \(2 \pi\)
\(|2x-1|>5\)
Indicate all such numbers
A. \(- \pi\)
B. \(- \frac{3}{2}
\)
C. \(- \sqrt{10}
\)
D. \(\frac{\sqrt{2}}{2}\)
E. \(2 \pi\)
Which of the following numbers satisfies the absolute value inequality
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13 Feb 2022, 19:40
13 Feb 2022, 19:40
2
\(|2x-1|>5\)
\(2x - 1 > 5\) & \(-5 > 2x - 1\)
\(2x > 6\) & \(2x < -4\)
\(x > 3\) & \(x < -2\)
From the options, only \(-\pi\), \(- \sqrt{10}\) & \(2 \pi\) will satisfy the range.
Answer A C E
\(2x - 1 > 5\) & \(-5 > 2x - 1\)
\(2x > 6\) & \(2x < -4\)
\(x > 3\) & \(x < -2\)
From the options, only \(-\pi\), \(- \sqrt{10}\) & \(2 \pi\) will satisfy the range.
Answer A C E
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Which of the following numbers satisfies the absolute value inequality
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15 Feb 2022, 06:53
15 Feb 2022, 06:53
1
Carcass wrote:
Which of the following numbers satisfies the absolute value inequality shown?
\(|2x-1|>5\)
Indicate all such numbers
A. \(- \pi\)
B. \(- \frac{3}{2}
\)
C. \(- \sqrt{10}
\)
D. \(\frac{\sqrt{2}}{2}\)
E. \(2 \pi\)
\(|2x-1|>5\)
Indicate all such numbers
A. \(- \pi\)
B. \(- \frac{3}{2}
\)
C. \(- \sqrt{10}
\)
D. \(\frac{\sqrt{2}}{2}\)
E. \(2 \pi\)
When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive
So, if \(|2x-1|>5\), we can conclude that EITHER \(2x-1>5\) OR \(2x-1< -5\)
Now let's solve each of the resulting inequalities:
Take: \(2x-1>5\)
Add 1 to both sides: \(2x>6\)
Divide both sides by 2 to get: \(x>3\)
Take: \(2x-1<-5\)
Add 1 to both sides: \(2x<-4\)
Divide both sides by 2 to get: \(x<-2\)
So, we're looking for any answer choice that satisfies either inequality (\(x>3\) or \(x<-2\))
A. \(- \pi ≈ -3.14\). This satisfies the inequality \(x<-2\)
B. \(- \frac{3}{2} = -1.5\). This satisfies neither inequality.
C. \(- \sqrt{10}≈ -3.something\). This satisfies the inequality \(x<-2\)
D. \(\frac{\sqrt{2}}{2}≈\frac{1.4}{2}≈0.7\). This satisfies neither inequality.
E. \(2 \pi\)≈(2)(3.14) ≈ 6.28[/quote]. This satisfies the inequality \(x>3\)
Answer: A, C and E
