Question

1. writing in math explain how solving -5x < 25 is different from solving 5x < 25.

there is also some partial text about another inequality: \...solves the inequality 5n > -25. he says the...\ but the main question is about comparing solving -5x < 25 and 5x < 25

Explanation:

Step1: Solve \(5x < 25\)

To solve \(5x < 25\), we divide both sides by 5 (a positive number). When dividing an inequality by a positive number, the direction of the inequality sign remains the same.
\(\frac{5x}{5} < \frac{25}{5}\)
\(x < 5\)

Step2: Solve \(-5x < 25\)

To solve \(-5x < 25\), we divide both sides by \(-5\) (a negative number). When dividing an inequality by a negative number, the direction of the inequality sign must be reversed.
\(\frac{-5x}{-5} > \frac{25}{-5}\)
\(x > -5\)

Answer:

When solving \(5x < 25\), we divide by 5 (positive) and the inequality sign stays, giving \(x < 5\). When solving \(-5x < 25\), we divide by \(-5\) (negative) and reverse the inequality sign, giving \(x > -5\). The key difference is the reversal of the inequality sign when dividing by a negative number.