To solve the inequality [tex]\(5 - 2x < 8x - 3\)[/tex], we aim to isolate the variable [tex]\(x\)[/tex] on one side of the inequality. Here is a step-by-step explanation of how we can do this:
1. Start with the original inequality:
[tex]\[
5 - 2x < 8x - 3
\][/tex]
2. The goal is to isolate the variable [tex]\(x\)[/tex]. To do this, we need to move all the terms involving [tex]\(x\)[/tex] to one side of the inequality and the constant terms to the other side. One efficient way to start is by removing the [tex]\(-2x\)[/tex] from the left side. We can do this by adding [tex]\(2x\)[/tex] to both sides of the inequality:
[tex]\[
5 - 2x + 2x < 8x - 3 + 2x
\][/tex]
3. Simplify both sides of the inequality:
[tex]\[
5 < 10x - 3
\][/tex]
Now, we have isolated the [tex]\(x\)[/tex]-terms on the right side. Thus, the correct first step in solving the inequality [tex]\(5 - 2x < 8x - 3\)[/tex] is:
[tex]\[
5 < 10x - 3
\][/tex]
This corresponds to the third option in the multiple choices provided. Therefore, the correct first step in solving the inequality is:
[tex]\[ \boxed{3} \][/tex]
