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Elina [12.6K]
3 years ago
14

Solve: |2x + 3| -1 < 4

Mathematics
2 answers:
lara [203]3 years ago
8 0
Add 1
  |2x +3| < 5
Unfold
  -5 < 2x +3 < 5
Subtract 3
  -8 < 2x < 2
Divide by 2
  -4 < x < 1

The solution is
  -4 < x < 1

_____
If you subtract 4 from both sides, you get an expression that compares to zero. Most graphing calculators will show you the zero-crossings, so you can easily find the values of x where this is true.

dybincka [34]3 years ago
7 0
|2x+3|-1<4
|2x+3|<5

1) when 2x +3 is positive     
2x+3<5
2x<2
x<1    (-∞, 1)

2) when 2x+3 is negative
-(2x+3)<5
-2x-3<5
-2x<8
x>-4  (-4, ∞)

(-∞, 1)∩(-4, ∞)=(-4,1)



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21/8 as a mixed number
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8 0
3 years ago
A. Student GPAs: Bob’s z-score z = + 1.71 μ = 2.98 σ = 0.36 b. Weekly work hours: Sarah’s z-score z = + 1.18 μ = 21.6 σ = 7.1 c.
hjlf

Answer:

a) x = \mu +z*\sigma

And replacing we got:

x= 2.98 + 1.71*0.36 = 3.5956

b) x = \mu +z*\sigma

And replacing we got:

x= 21.6 + 1.18*7.1 = 29.978

c) x = \mu -z*\sigma

And replacing we got:

x= 150 - 1.35*40= 96

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable of interest for this case. We define the z score with the following formula:

z=\frac{x-\mu}{\sigma}

And for this case we know that z = 1.71, \mu = 2.98,\sigma = 0.36

If we solve for x from the z score formula we got:

x = \mu +z*\sigma

And replacing we got:

x= 2.98 + 1.71*0.36 = 3.5956

Part b

Let X the random variable of interest for this case. We define the z score with the following formula:

z=\frac{x-\mu}{\sigma}

And for this case we know that z = 1.18, \mu = 21.6,\sigma = 7.1

If we solve for x from the z score formula we got:

x = \mu +z*\sigma

And replacing we got:

x= 21.6 + 1.18*7.1 = 29.978

Part c

Let X the random variable of interest for this case. We define the z score with the following formula:

z=\frac{x-\mu}{\sigma}

And for this case we know that z = -1.35, \mu = 150,\sigma = 40

If we solve for x from the z score formula we got:

x = \mu -z*\sigma

And replacing we got:

x= 150 - 1.35*40= 96

5 0
3 years ago
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