Question

solve the inequality and graph the solution.
-3 + 2n ≤ 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)--->
submit

Explanation:

Step1: Add 3 to both sides

To isolate the term with \( n \), we add 3 to both sides of the inequality \(-3 + 2n \leq 1\). This gives us \(-3 + 3+ 2n \leq 1 + 3\), which simplifies to \(2n \leq 4\).

Step2: Divide by 2

Next, we divide both sides of the inequality \(2n \leq 4\) by 2 to solve for \( n \). So, \(\frac{2n}{2} \leq \frac{4}{2}\), which simplifies to \(n \leq 2\).

Answer:

The solution to the inequality \(-3 + 2n \leq 1\) is \(n \leq 2\). To graph this, we plot a closed dot at \( n = 2 \) (since the inequality is "less than or equal to") and draw a ray to the left of 2 on the number line.