Question

solve the inequality and graph the solution.
1 > \\(\frac{y}{-2}\\) + 3
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.
-5 -4 -3 -2 -1 0 1 2 3 4 5

Explanation:

Step1: Subtract 3 from both sides

To isolate the term with \( y \), we subtract 3 from both sides of the inequality \( 1 > \frac{y}{-2} + 3 \). This gives us \( 1 - 3 > \frac{y}{-2} + 3 - 3 \), which simplifies to \( -2 > \frac{y}{-2} \).

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

When we multiply or divide an inequality by a negative number, we must reverse the inequality sign. So, multiplying both sides of \( -2 > \frac{y}{-2} \) by -2 gives \( (-2) \times (-2) < y \) (note the reversed inequality). Calculating the left side, we get \( 4 < y \), or equivalently \( y > 4 \).

Answer:

The solution to the inequality is \( y > 4 \). To graph this, plot an open circle at 4 (since the inequality is strict, \( y
eq 4 \)) and draw an arrow to the right (indicating all values greater than 4).