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:
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
