To solve the inequality [tex]\(8z + 3 - 2z < 51\)[/tex], let's proceed step-by-step:
1. Combine like terms: Start by combining the terms involving [tex]\(z\)[/tex] on the left side.
[tex]\[8z - 2z + 3 < 51\][/tex]
2. Simplify the inequality: Perform the subtraction to simplify the expression.
[tex]\[6z + 3 < 51\][/tex]
3. Isolate the term with [tex]\(z\)[/tex]:
- Subtract 3 from both sides of the inequality to move the constant term to the right side.
[tex]\[6z + 3 - 3 < 51 - 3\][/tex]
[tex]\[6z < 48\][/tex]
4. Solve for [tex]\(z\)[/tex]:
- Divide both sides by 6 to isolate [tex]\(z\)[/tex].
[tex]\[\frac{6z}{6} < \frac{48}{6}\][/tex]
[tex]\[z < 8\][/tex]
Therefore, the solution to the inequality is [tex]\(z < 8\)[/tex].
Among the given options, the best answer is:
B. [tex]\(z < 8\)[/tex]
