Question

1. solve the inequality and graph the solution.

$2 < \frac{m}{-2} + 1$
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.
(number line with -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 marked)

Explanation:

Step1: Subtract 1 from both sides

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

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

When multiplying an inequality by a negative number, the inequality sign reverses. So we multiply both sides by -2:
\( 1 \times (-2) > \frac{m}{-2} \times (-2) \)
Simplifying gives \( -2 > m \), or equivalently \( m < -2 \).

Answer:

The solution to the inequality is \( m < -2 \). To graph this, plot an open circle at \( -2 \) on the number line and draw an arrow pointing to the left (towards more negative numbers).