Please solve and show work! Thanks!
1) lx - 5l > 4
3) 1 < lx-1l ≤ 5

Please note that lxl the l part is absolute value
Please solve for the inequality of x

Will give 5 star ratings and thanks along with brainleist (brainleist too best answer)

1) x < 1, x > 9

2) 2 < x ≤ 6, -4 ≤ x < 0

Step-by-step explanation:

1) lx - 5l > 4

x - 5 = 4

x = 9

-(x - 5) = 4

x = -4 + 5 = 1

x < 1, x > 9

3) 1 < lx-1l ≤ 5

1 < x-1 ≤ 5

2 < x ≤ 6

1 < -(x-1) ≤ 5

-5 ≤ x-1 < -1

-4 ≤ x < 0

1  x<1  or x>9

2 -4 ≤ x < 0  or 2 < x ≤ 6  

Step-by-step explanation:

1) lx - 5l > 4

When we have absolute values, we end up with 2 inequalities, one positive and one negative.  Remember when we have the negative inequality we have to flip the inequality symbol

x - 5 > 4      or         x - 5 <- 4

We use or since the absolute value is on the greater than side

Add 5 to each side

x - 5+5 > 4+5    or          x - 5+5 <- 4+5

x>9                  or                       x < 1

3) 1 < lx-1l ≤ 5

We will again have 2 equations , one positive and one negative (remembering to flip the inequalities on the negative)

1 < x-1 ≤ 5    or   -1 > x-1 ≥ -5

Add 1 to all sides

1+1 < x-1+1 ≤ 5+1    or  -1+1 > x-1+1 ≥ -5+1

2 < x ≤ 6          or          0 > x  ≥ -4

Rewriting

-4 ≤ x < 0  or 2 < x ≤ 6    

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.

your answer would be 12