To solve the inequality [tex]\(3x - 4 \geq 8\)[/tex], follow these steps:
1. Isolate the term with the variable (x):
Start by eliminating the constant term on the left-hand side. To do that, add 4 to both sides of the inequality:
[tex]\[
3x - 4 + 4 \geq 8 + 4
\][/tex]
2. Simplify the inequality:
The left-hand side becomes [tex]\(3x\)[/tex] and the right-hand side becomes [tex]\(12\)[/tex]:
[tex]\[
3x \geq 12
\][/tex]
3. Solve for x:
To isolate [tex]\(x\)[/tex], divide both sides of the inequality by 3:
[tex]\[
\frac{3x}{3} \geq \frac{12}{3}
\][/tex]
4. Simplify the result:
This simplifies to:
[tex]\[
x \geq 4
\][/tex]
So, the solution to the inequality [tex]\(3x - 4 \geq 8\)[/tex] is [tex]\(x \geq 4\)[/tex].
