Question

solve the inequality and graph the solution.

-y + 5 ≥ 1

plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

<---(-5)---(-4)---(-3)---(-2)---(-1)---(0)---(1)---(2)---(3)---(4)---(5)--->

Explanation:

Step1: Subtract 5 from both sides

To isolate the term with \( y \), we subtract 5 from both sides of the inequality \(-y + 5 \geq 1\). This gives us \(-y + 5 - 5 \geq 1 - 5\), which simplifies to \(-y \geq -4\).

Step2: Multiply both sides by -1 (reverse inequality)

When we multiply or divide both sides of an inequality by a negative number, we must reverse the inequality sign. So, multiplying both sides of \(-y \geq -4\) by -1 gives \( y \leq 4 \).

Answer:

The solution to the inequality \(-y + 5 \geq 1\) is \( y \leq 4 \). To graph this, we plot a closed dot at \( 4 \) (since the inequality is "less than or equal to") and draw a ray to the left of \( 4 \) to represent all values of \( y \) that are less than or equal to \( 4 \).