To solve the inequality [tex]\(2x - 9 \leq 1\)[/tex], follow these steps:
1. Isolate the term involving [tex]\(x\)[/tex]:
Add 9 to both sides of the inequality to cancel out the -9 on the left-hand side:
[tex]\[
2x - 9 + 9 \leq 1 + 9
\][/tex]
Simplifying this, we get:
[tex]\[
2x \leq 10
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], divide both sides of the inequality by 2:
[tex]\[
\frac{2x}{2} \leq \frac{10}{2}
\][/tex]
Simplifying this, we obtain:
[tex]\[
x \leq 5
\][/tex]
Hence, the solution to the inequality [tex]\(2x - 9 \leq 1\)[/tex] is:
[tex]\[
x \leq 5
\][/tex]
In interval notation, this is represented as:
[tex]\[
(-\infty, 5]
\][/tex]
This tells us that [tex]\(x\)[/tex] can be any real number less than or equal to 5.
