To solve the inequality [tex]\(-4x + 18 \geq 6\)[/tex], we will follow a series of algebraic steps to isolate the variable [tex]\(x\)[/tex].
Step 1: Subtract 18 from both sides of the inequality
First, we subtract 18 from both sides to get rid of the constant term on the left-hand side:
[tex]\[
-4x + 18 - 18 \geq 6 - 18
\][/tex]
This simplifies to:
[tex]\[
-4x \geq -12
\][/tex]
Step 2: Divide both sides by -4
Next, we need to isolate [tex]\(x\)[/tex] by dividing both sides of the inequality by -4. Remember, when dividing or multiplying an inequality by a negative number, we must flip the inequality sign:
[tex]\[
-4x / -4 \leq -12 / -4
\][/tex]
This simplifies to:
[tex]\[
x \leq 3
\][/tex]
Thus, the solution to the inequality [tex]\(-4x + 18 \geq 6\)[/tex] is:
[tex]\[
x \leq 3
\][/tex]
