solve the compound inequality
0<2x-4<8
two parts to this problem
1) 2x-4> 0
2) 2x-4 <8
solve each separately
1) 2x > 4
x>2
2) 2x<12
x<6
if x is greater than 2 and less than 6 write it like this: 2<x<6
I solve these all together by adding 4 to all 3 parts and then dividing all 3 parts by 2.
that way, I don't have to worry about the directions of the inequalities.
0<2x-4 <8
4<2x<12
2<x<6
To solve the compound inequality 0 < 2x - 4 < 8, we need to isolate x by performing the same operation on all parts of the compound inequality.
Step 1: Add 4 to all parts of the inequality:
0 + 4 < 2x - 4 + 4 < 8 + 4
This simplifies to:
4 < 2x < 12
Now we have a simple inequality with a single variable.
Step 2: Divide all parts of the inequality by 2:
4/2 < (2x)/2 < 12/2
This simplifies to:
2 < x < 6
Hence, the solution to the compound inequality 0 < 2x - 4 < 8 is x ∈ (2, 6).