Let's solve the inequality step by step:
The given inequality is:
[tex]\[ 5 - 2x < 8x - 3 \][/tex]
A common first step in solving inequalities is to get all terms involving the variable [tex]\( x \)[/tex] on one side and the constant terms on the other side. This helps in isolating the variable, making it easier to solve.
1. We should move the term [tex]\(-2x\)[/tex] to the right side. To do this, add [tex]\( 2x \)[/tex] to both sides:
[tex]\[ 5 - 2x + 2x < 8x - 3 + 2x \][/tex]
[tex]\[ 5 < 10x - 3 \][/tex]
So the inequality simplifies to:
[tex]\[ 5 < 10x - 3 \][/tex]
Hence, the correct first step is transforming the inequality to:
[tex]\[ 5 < 10x - 3 \][/tex]
Thus, the correct choice is:
[tex]\[ 5 < 10x - 3 \][/tex]
