Question

Please solve and show work! Thanks!

Answer 1

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

Answer 2

Answer:

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