To solve the inequality [tex]\(-6 \geq 10 - 4x\)[/tex], follow these steps:
1. Isolate the term containing the variable [tex]\(x\)[/tex]:
Start by subtracting [tex]\(10\)[/tex] from both sides of the inequality:
[tex]\[
-6 - 10 \geq 10 - 4x - 10
\][/tex]
Simplify both sides:
[tex]\[
-16 \geq -4x
\][/tex]
2. Solve for [tex]\(x\)[/tex]:
Now, you need to isolate [tex]\(x\)[/tex] by dividing both sides by [tex]\(-4\)[/tex]. Remember, when you divide or multiply both sides of an inequality by a negative number, you must reverse the direction of the inequality:
[tex]\[
\frac{-16}{-4} \leq \frac{-4x}{-4}
\][/tex]
Simplify both sides:
[tex]\[
4 \leq x
\][/tex]
or equivalently:
[tex]\[
x \geq 4
\][/tex]
Hence, the solution to the inequality [tex]\(-6 \geq 10 - 4x\)[/tex] is [tex]\(x \geq 4\)[/tex].
Therefore, the correct answer is:
[tex]\[
x \geq 4
\][/tex]
