Question

solve the inequality and graph the solution.
10 + 3j ≥ 4
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 10 from both sides

To isolate the term with \( j \), we subtract 10 from both sides of the inequality \( 10 + 3j \geq 4 \). This gives us \( 10 + 3j - 10 \geq 4 - 10 \), which simplifies to \( 3j \geq -6 \).

Step2: Divide both sides by 3

To solve for \( j \), we divide both sides of the inequality \( 3j \geq -6 \) by 3. Since 3 is a positive number, the direction of the inequality sign remains the same. So we have \( \frac{3j}{3} \geq \frac{-6}{3} \), which simplifies to \( j \geq -2 \).

Answer:

The solution to the inequality \( 10 + 3j \geq 4 \) is \( j \geq -2 \). To graph this, we plot a closed dot at \( -2 \) (because the inequality is "greater than or equal to") and draw a ray to the right of \( -2 \) on the number line.