To solve the inequality [tex]\(-6a + 45 \leq 3\)[/tex], follow these steps:
1. Isolate the variable term:
[tex]\[
-6a + 45 \leq 3
\][/tex]
2. Subtract 45 from both sides to move the constant term to the right side:
[tex]\[
-6a + 45 - 45 \leq 3 - 45
\][/tex]
Simplifying this, we get:
[tex]\[
-6a \leq -42
\][/tex]
3. Divide both sides by -6 to solve for [tex]\(a\)[/tex]. Note that dividing by a negative number reverses the direction of the inequality:
[tex]\[
a \geq \frac{-42}{-6}
\][/tex]
Simplifying this, we get:
[tex]\[
a \geq 7
\][/tex]
So the solution to the inequality [tex]\(-6a + 45 \leq 3\)[/tex] is [tex]\(a \geq 7\)[/tex].
This means that any value [tex]\(a\)[/tex] satisfying [tex]\(a \geq 7\)[/tex] is a solution to the inequality. In interval notation, the solution set is:
[tex]\[
[7, \infty)
\][/tex]
