Question

How would you solve these compound inequalities?
1. -1<4x-3<5
2. 3a-5<=-2 OR 3a-5>=13
3. -y-2>6 OR 4y+8<=20
4. 3<=-2x+1<=9

Answer 1

for the 1st and last
"whatever you do to the middle, do to the left and right"

1.
-1<4x-3<5
add 3
2 < 4x < 8
divide by +4, no change of inequality signs neede

1/2 < x < 2

6.
3 ≤ -2x + 1 ≤ 9
add 1
4 ≤ -2x ≥ 10
divide by -2, ahhh, must switch signs
-2 ≥ x ≥ -5
or
-5 ≤ x ≤ -2

2. 3a-5 ≤ 2 OR 3a - 5 ≥ 13
3a ≤ 7 OR 3x ≥ 18
a ≤ 7/3 OR x ≥ 6

do #3 the same way as #2
watch the change of signs for the first part