To solve the inequality [tex]\(8z + 3 - 2z < 51\)[/tex], let's go through the process step by step.
1. Combine like terms on the left-hand side:
[tex]\[
8z - 2z + 3 < 51
\][/tex]
This simplifies to:
[tex]\[
6z + 3 < 51
\][/tex]
2. Isolate the variable term:
Subtract 3 from both sides to get:
[tex]\[
6z < 48
\][/tex]
3. Solve for the variable:
Divide both sides by 6:
[tex]\[
z < 8
\][/tex]
So, the solution to the inequality [tex]\(8z + 3 - 2z < 51\)[/tex] is [tex]\(z < 8\)[/tex]. This means that the value of [tex]\(z\)[/tex] can be any number less than 8.
Therefore, the best choice among the given options is:
C. [tex]\(z < 8\)[/tex]
