A compound inequality is the combination of one or more inequalities.
The solution to [tex]\mathbf{6 < 4x - 2(x - 2) \le 12}[/tex] is [tex]\mathbf{5< x \le 8}[/tex]
The inequality is given as:
[tex]\mathbf{6 < 4x - 2(x - 2) \le 12}[/tex]
Open bracket
[tex]\mathbf{6 < 4x - 2x - 4 \le 12}[/tex]
[tex]\mathbf{6 < 2x - 4 \le 12}[/tex]
Add 4 to all three sides
[tex]\mathbf{6 +4< 2x - 4 + 4\le 12 + 4}[/tex]
[tex]\mathbf{10< 2x \le 16}[/tex]
Divide through by 2
[tex]\mathbf{5< x \le 8}[/tex]
Hence, the solution to [tex]\mathbf{6 < 4x - 2(x - 2) \le 12}[/tex] is [tex]\mathbf{5< x \le 8}[/tex]
See attachment for the number line of [tex]\mathbf{5< x \le 8}[/tex]
Read more about compound inequalities at:
https://brainly.com/question/17957246
