Question

1. $-2 + \frac{5}{4}x geq -12$

Explanation:

Step1: Add 2 to both sides

To isolate the term with \( x \), we add 2 to both sides of the inequality \( -2 + \frac{5}{4}x \geq -12 \). This gives us \( \frac{5}{4}x \geq -12 + 2 \), which simplifies to \( \frac{5}{4}x \geq -10 \).

Step2: Multiply by reciprocal

To solve for \( x \), we multiply both sides by the reciprocal of \( \frac{5}{4} \), which is \( \frac{4}{5} \). So, \( x \geq -10 \times \frac{4}{5} \). Calculating the right - hand side, \( -10\times\frac{4}{5}=\frac{-40}{5}=-8 \). So we get \( x \geq - 8 \).

Answer:

\( x \geq -8 \)