![-6](https://tex.z-dn.net/?f=-6%3C4x%2B2%3C6%5Cquad%20%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3A-2%3Cx%3C1%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%5Cleft%28-2%2C%5C%3A1%5Cright%29%5Cend%7Bbmatrix%7D)
<em><u>Solution:</u></em>
<em><u>Given conjunction is:</u></em>
![-6](https://tex.z-dn.net/?f=-6%3C4x%2B2%3C6)
We have to find the solution set
<em><u>Let us solve the given conjuction</u></em>
![\mathrm{If}\:a](https://tex.z-dn.net/?f=%5Cmathrm%7BIf%7D%5C%3Aa%3Cu%3Cb%5C%3A%5Cmathrm%7Bthen%7D%5C%3Aa%3Cu%5C%20%5Cmathrm%7Band%7D%5C%20%5C%3Au%3Cb)
Therefore,
![-6](https://tex.z-dn.net/?f=-6%3C4x%2B2%5Cquad%20%5Cmathrm%7Band%7D%5Cquad%20%5C%3A4x%2B2%3C6)
<h3><em><u>
Let us first solve -6 < 4x + 2</u></em></h3>
![-6 < 4x + 2](https://tex.z-dn.net/?f=-6%20%3C%204x%20%2B%202)
Switch the sides by flipping the inequality symbol
![4x+2>-6](https://tex.z-dn.net/?f=4x%2B2%3E-6)
![\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\\\4x+2-2>-6-2\\\\\mathrm{Simplify}\\\\4x>-8\\\\\mathrm{Divide\:both\:sides\:by\:}4\\\\\frac{4x}{4}>\frac{-8}{4}](https://tex.z-dn.net/?f=%5Cmathrm%7BSubtract%5C%3A%7D2%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C%5C%5C4x%2B2-2%3E-6-2%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5C4x%3E-8%5C%5C%5C%5C%5Cmathrm%7BDivide%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D4%5C%5C%5C%5C%5Cfrac%7B4x%7D%7B4%7D%3E%5Cfrac%7B-8%7D%7B4%7D)
![x>-2](https://tex.z-dn.net/?f=x%3E-2)
<h3><u><em>Now let us solve 4x + 2 < 6</em></u></h3>
![4x+2](https://tex.z-dn.net/?f=4x%2B2%3C6%5C%5C%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D2%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C%5C%5C4x%2B2-2%3C6-2%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5C4x%3C4%5C%5C%5C%5C%5Cmathrm%7BSimplify%7D%5C%5C%5C%5Cx%3C1)
![\mathrm{Combine\:the\:intervals}](https://tex.z-dn.net/?f=%5Cmathrm%7BCombine%5C%3Athe%5C%3Aintervals%7D)
![x>-2\quad \mathrm{and}\quad \:x](https://tex.z-dn.net/?f=x%3E-2%5Cquad%20%5Cmathrm%7Band%7D%5Cquad%20%5C%3Ax%3C1)
![Merge\:Overlapping\:Intervals](https://tex.z-dn.net/?f=Merge%5C%3AOverlapping%5C%3AIntervals)
![-2](https://tex.z-dn.net/?f=-2%3Cx%3C1)
<h3><u>Thus the solution set for –6 < 4x + 2 < 6 is:</u></h3>
![-6](https://tex.z-dn.net/?f=-6%3C4x%2B2%3C6%5Cquad%20%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3A-2%3Cx%3C1%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%5Cleft%28-2%2C%5C%3A1%5Cright%29%5Cend%7Bbmatrix%7D)
Eh theres 52 cards in a deck and samsung is 7 words/cards and theres 4 queens in a deck soooo 52 divided by 4 is 13 and theres 13 total diffrent cards soooooooo uh it should be a 7.428 percent chance
Answer:
![4\sqrt{6} feet](https://tex.z-dn.net/?f=4%5Csqrt%7B6%7D%20feet)
Step-by-step explanation:
<u>Step 1: Make an equation to represent the scenario
</u>
![a^2 + b^2 = c^2](https://tex.z-dn.net/?f=a%5E2%20%2B%20b%5E2%20%3D%20c%5E2)
![(2)^2 + b^2 = (10)^2](https://tex.z-dn.net/?f=%282%29%5E2%20%2B%20b%5E2%20%3D%20%2810%29%5E2)
![4 + b^2 - 4 = 100 - 4](https://tex.z-dn.net/?f=4%20%2B%20b%5E2%20-%204%20%3D%20100%20-%204)
![b^2 = 96](https://tex.z-dn.net/?f=b%5E2%20%3D%2096)
<u>Step 2: Square root both sides
</u>
<u />![\sqrt{b^2} = \sqrt{96}](https://tex.z-dn.net/?f=%5Csqrt%7Bb%5E2%7D%20%3D%20%5Csqrt%7B96%7D)
![b = \sqrt{4^2*6}](https://tex.z-dn.net/?f=b%20%3D%20%5Csqrt%7B4%5E2%2A6%7D)
![b=4\sqrt{6}](https://tex.z-dn.net/?f=b%3D4%5Csqrt%7B6%7D)
Answer: ![4\sqrt{6} feet](https://tex.z-dn.net/?f=4%5Csqrt%7B6%7D%20feet)
Answer:
inches
Step-by-step explanation:
The "to" unit goes in the numerator. (The "from" unit goes in the denominator.) Since we're converting to inches, the numerator of the conversion factor has units of inches.
_____
9 yd = 9 yd × (36 in)/(1 yd) = 324 in
Answer:
(2,1)
Step-by-step explanation:
Because it rises by 2 and runs by 1