To solve the inequality [tex]\(5 < 8x < 2x + 3\)[/tex], let's break down the steps in detail to identify the missing step.
1. Understand the given inequality:
We start with the compound inequality:
[tex]\[5 < 8x < 2x + 3\][/tex]
2. Isolate the term involving [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], we need to move all terms involving [tex]\( x \)[/tex] to one side.
3. Perform the missing step:
The operation needed to isolate [tex]\( x \)[/tex] involves removing [tex]\( 2x \)[/tex] from the rightmost part of the inequality.
We need to subtract [tex]\( 2x \)[/tex] from both sides of the inequality:
[tex]\[5 < 8x - 2x < 2x + 3 - 2x\][/tex]
4. Simplify the inequality:
Simplifying the inequality after subtracting [tex]\( 2x \)[/tex]:
[tex]\[5 < 6x < 3\][/tex]
Therefore, the correct missing step in solving the inequality is to subtract [tex]\( 2x \)[/tex] from both sides of the inequality.
