Question

solve the linear inequality for k. graph your answer in the number line. then write the solution in inequality notation.
7 ≥ 3k + 1
show your work here
hint: to add infinity (∞), type \infinity\

Explanation:

Step1: Subtract 1 from both sides

$7 - 1 \geq 3k + 1 - 1$
$6 \geq 3k$

Step2: Divide by 3 on both sides

$\frac{6}{3} \geq \frac{3k}{3}$
$2 \geq k$

Step3: Rewrite for standard notation

$k \leq 2$

Number Line Graph Description:

Draw a closed circle at 2 (since the inequality includes equality), and shade all points to the left of 2, extending towards negative infinity.

Answer:

Inequality notation: $k \leq 2$
Number line: Closed circle at 2, shading to the left (towards $-\text{infinity}$)