Which of the following are solutions to |x-1|= 5x + 2? check all that apply.
a: x=3/4
b: x=3/4, 1/6
c: x= -1/6
d: x= 1/6

The solution of |x-1| = 5x + 2 is and option c is correct.

Solution:

Given, equation is |x-1|= 5x + 2

We have to find the value of x  

Now, |x-1|= 5x + 2  

Because mod becomes "±" when shifted to opposite side of “=”

x – 1 = ±(5x+2)    

x – 1 = 5x + 2 or x – 1 = -(5x + 2)

In options we have only

Hence, the value of x is and option c is correct

f(x) is going down by 4

step-by-step explanation:

(its either that or its going left by 4)

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.