Solve for [tex]\( a \)[/tex]:

[tex]\[ -6a + 45 \leq 3 \][/tex]

A. [tex]\( a \geq -8 \)[/tex]
B. [tex]\( a \geq 7 \)[/tex]
C. [tex]\( a \geq -7 \)[/tex]
D. [tex]\( a \leq 7 \)[/tex]



Answer :

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]