To solve the inequality [tex]\(-5x + 2 \leq 12\)[/tex], we need to isolate the variable [tex]\(x\)[/tex]. Let's go through the steps one by one:
1. Subtract 2 from both sides:
[tex]\[
-5x + 2 - 2 \leq 12 - 2
\][/tex]
Simplify the expression:
[tex]\[
-5x \leq 10
\][/tex]
2. Divide both sides by -5:
When dividing both sides of an inequality by a negative number, we must reverse the inequality sign.
[tex]\[
\frac{-5x}{-5} \geq \frac{10}{-5}
\][/tex]
Simplify the expression:
[tex]\[
x \geq -2
\][/tex]
Putting it all together, the solution to the inequality [tex]\(-5x + 2 \leq 12\)[/tex] is:
[tex]\[
x \geq -2
\][/tex]
In interval notation, this can be written as:
[tex]\[
[-2, \infty)
\][/tex]
So, the solution is [tex]\(-2 \leq x < \infty\)[/tex].
