solve the compound inequality
< 2x-4<8
You are missing something.
To solve the compound inequality <2x - 4 < 8, you need to find the range of values for x that satisfy both parts of the inequality.
First, let's isolate x by adding 4 to all parts of the inequality:
<2x - 4 + 4 < 8 + 4
<2x < 12
Next, divide all parts of the inequality by 2 to solve for x:
<2x/2 < 12/2
x < 6
So the first part of the compound inequality is x < 6.
Now, let's focus on the second inequality:
< 2x - 4 > -8
We'll isolate x by adding 4 to all parts of the inequality:
< 2x - 4 + 4 > -8 + 4
< 2x > -4
Next, divide all parts of the inequality by 2 to solve for x:
< 2x/2 > -4/2
< x > -2
So the second part of the compound inequality is x > -2.
Combining the two parts, we have x < 6 and x > -2.
Therefore, the solution to the compound inequality <2x - 4 < 8 is -2 < x < 6.