Answer:
D. I or II only
Step-by-step explanation:
By a small online search, I've found that the equation is:
6x + 7 = 3x - 5
And the options are:
I. Combining the 6x and 3x terms
II. Combining the 7 and 5
III. Dividing both sides of the equation by 6
A. I only
B. II only
C. III only
D. I or II only
E. I or II or III
So, let's solve the equation in such a way that we can prevent the use of fractions:
6x + 7 = 3x - 5
We can use I and II, combining one in each side, so we get (so we use I and II at the same time)
6x - 3x = -5 - 7
solving these, we get:
(6 - 3)*x = -12
3*x = -12
and -12 is divisible by 3, so if we divide in both sides by 3, we get:
x = -12/3 = -4
x = -4
So we avoided working with fractions, and we used I and II.
Then the first step could be either I or II (the order does not matter)
Then the correct option is:
D. I or II only
let's firstly convert the mixed fractions to improper fractions, and then subtract.
![\bf \stackrel{mixed}{5\frac{1}{4}}\implies \cfrac{5\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{21}{4}}~\hfill \stackrel{mixed}{3\frac{2}{3}}\implies \cfrac{3\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{11}{3}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{21}{4}-\cfrac{11}{3}\implies \stackrel{\textit{we'll use the LCD of 12}}{\cfrac{(3)21-(4)11}{12}}\implies \cfrac{63-44}{12}\implies \cfrac{19}{12}\implies 1\frac{7}{12}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B5%5Cfrac%7B1%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B5%5Ccdot%204%2B1%7D%7B4%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B21%7D%7B4%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B3%5Cfrac%7B2%7D%7B3%7D%7D%5Cimplies%20%5Ccfrac%7B3%5Ccdot%203%2B2%7D%7B3%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B11%7D%7B3%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Ccfrac%7B21%7D%7B4%7D-%5Ccfrac%7B11%7D%7B3%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bwe%27ll%20use%20the%20LCD%20of%2012%7D%7D%7B%5Ccfrac%7B%283%2921-%284%2911%7D%7B12%7D%7D%5Cimplies%20%5Ccfrac%7B63-44%7D%7B12%7D%5Cimplies%20%5Ccfrac%7B19%7D%7B12%7D%5Cimplies%201%5Cfrac%7B7%7D%7B12%7D)
Answer: 
Step-by-step explanation:
Given the following equation:

You can follow these steps in order to solve for "x" and find its value:
1. Apply Distributive property on the right side of the equation:

2. Subract
from both sides and add the like terms:

3. Subtract 1.8 from both sides:

4. Finally, divide both side of the equation by -1.5:

Answer:
or 
Step-by-step explanation:
the given function is;

According to the rational roots theorem, the possible rational roots are;
.
According to the Remainder Theorem, if
, then
is a zero of the polynomial.



Also,



Therefore the other roots are;
