To solve the inequality [tex]\(-8x < 16\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Understand the inequality: We need to isolate the variable [tex]\(x\)[/tex] on one side of the inequality sign.
2. Divide both sides by [tex]\(-8\)[/tex]: Since we are dividing by a negative number, it is important to remember that dividing or multiplying both sides of an inequality by a negative number reverses the inequality sign.
[tex]\[
x > \frac{16}{-8}
\][/tex]
3. Simplify the right side: Perform the division on the right side of the inequality.
[tex]\[
x > -2
\][/tex]
So, the solution to the inequality [tex]\( -8x < 16 \)[/tex] is [tex]\( x > -2 \)[/tex]. This means that any value of [tex]\(x\)[/tex] greater than [tex]\(-2\)[/tex] will satisfy the inequality.
