Solve the inequality: -2.6x – 20.8 ≤ -52.

Answer 1

To solve the inequality \(-2.6x - 20.8 \leq -52\), we can follow these steps:

1. Add 20.8 to both sides of the inequality:

   \[ -2.6x - 20.8 + 20.8 \leq -52 + 20.8 \]

   This simplifies to:

   \[ -2.6x \leq -31.2 \]

2. Divide both sides by -2.6. Remember that when we divide an inequality by a negative number, we must reverse the inequality sign:

   \[ x \geq \frac{-31.2}{-2.6} \]

   Calculating the division gives:

   \[ \frac{-31.2}{-2.6} = 12 \]

So, the solution to the inequality is:

\[ x \geq 12 \]

In interval notation, this can be expressed as:

\[ [12, \infty) \]