Question

1. solve the inequality and graph the solution.

$2 < \frac{m}{-4} + 1$
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.

Explanation:

Step1: Subtract 1 from both sides

To isolate the term with \( m \), we subtract 1 from both sides of the inequality \( 2 < \frac{m}{-2}+1 \). This gives us \( 2 - 1 < \frac{m}{-2}+1 - 1 \), which simplifies to \( 1 < \frac{m}{-2} \).

Step2: Multiply both sides by -2 (and reverse inequality)

When we multiply both sides of an inequality by a negative number, we must reverse the inequality sign. So, multiplying both sides of \( 1 < \frac{m}{-2} \) by -2 gives \( 1\times(-2) > \frac{m}{-2}\times(-2) \), which simplifies to \( - 2>m \) or \( m < - 2 \).

Answer:

The solution to the inequality is \( m < - 2 \). To graph this, we plot an open circle at \( - 2 \) (since the inequality is strict, \( m
eq - 2 \)) and draw an arrow to the left (indicating all values less than \( - 2 \)).