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]
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]