Answer:
![\left|x-3\right|](https://tex.z-dn.net/?f=%5Cleft%7Cx-3%5Cright%7C%3C5%5Cquad%20%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3A-2%3Cx%3C8%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%5Cleft%28-2%2C%5C%3A8%5Cright%29%5Cend%7Bbmatrix%7D)
The graph is also attached.
Step-by-step explanation:
Given the expression
![|x-3|\:](https://tex.z-dn.net/?f=%7Cx-3%7C%5C%3A%3C%5C%3A5)
Apply absolute rule:
![\mathrm{If}\:|u|\:0\:\mathrm{then}\:-a\:](https://tex.z-dn.net/?f=%5Cmathrm%7BIf%7D%5C%3A%7Cu%7C%5C%3A%3C%5C%3Aa%2C%5C%3Aa%3E0%5C%3A%5Cmathrm%7Bthen%7D%5C%3A-a%5C%3A%3C%5C%3Au%5C%3A%3C%5C%3Aa)
so the expression becomes
![-5](https://tex.z-dn.net/?f=-5%3Cx-3%3C5)
![x-3>-5\quad \mathrm{and}\quad \:x-3](https://tex.z-dn.net/?f=x-3%3E-5%5Cquad%20%5Cmathrm%7Band%7D%5Cquad%20%5C%3Ax-3%3C5)
solving condition 1
x−3<5
Add 3 to both sides
x−3+3<5+3
x<8
solving condition 2
x−3>−5
Add 3 to both sides
x−3+3>−5+3
x>−2
combining the intervals
![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%3C8)
Merging overlapping intervals
![-2](https://tex.z-dn.net/?f=-2%3Cx%3C8)
Therefore,
![\left|x-3\right|](https://tex.z-dn.net/?f=%5Cleft%7Cx-3%5Cright%7C%3C5%5Cquad%20%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3A-2%3Cx%3C8%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%5Cleft%28-2%2C%5C%3A8%5Cright%29%5Cend%7Bbmatrix%7D)
The graph is also attached.
For instance, the factors<span> of 15 are 3 and 5, because 3×5 = 15. Some </span>numbers<span> have more than one factorization (more than one way of being factored). For instance, 12 can be factored as 1×12, 2×6, or 3×4. A </span>number<span> that can only be factored as 1 times itself is called "prime".</span>
Answer:
The answer is option D.
Step-by-step explanation:
(4a - b)(2a - 3b)
Expand the terms
We have
8a² - 12ab - 2ab + 3b²
Which is
8a² - 14ab + 3b²
That's option D.
Hope this helps you
Check your solution by first checking the end point , in the related equation. Pick a value greater than , such as 2, to check in the inequality. Solve for x. Divide both sides by 3 to isolate the variable.