To determine the missing step in solving the given inequality:
[tex]\[ 5 < 8x < 2x + 3 \][/tex]
we need to isolate the variable [tex]\( x \)[/tex]. Let's proceed step-by-step:
1. Initially, the inequality is given as:
[tex]\[ 5 < 8x < 2x + 3 \][/tex]
2. We can break this into two separate inequalities for simplicity:
[tex]\[ 5 < 8x \][/tex]
[tex]\[ 8x < 2x + 3 \][/tex]
Focus on the second inequality:
[tex]\[ 8x < 2x + 3 \][/tex]
3. To isolate [tex]\( x \)[/tex], we need to move all terms involving [tex]\( x \)[/tex] to one side. A key step in solving this is to eliminate the [tex]\( 8x \)[/tex] on the left side.
4. Subtract [tex]\( 8x \)[/tex] from both sides to remove [tex]\( 8x \)[/tex] from the left:
[tex]\[ 8x - 8x < 2x + 3 - 8x \][/tex]
This simplifies to:
[tex]\[ 0 < -6x + 3 \][/tex]
So the necessary step to solve the inequality is:
Subtract [tex]\( 8x \)[/tex] from both sides of the inequality.
Thus, the correct answer is:
[tex]\[ \boxed{\text{Subtract } 8x \text{ from both sides of the inequality.}} \][/tex]
