Question

solve the linear inequality for ( k ). graph your answer in the number line. then write the solution in inequality notation.
( 7 geq 3k + 1 )

show your work here.

whats the solution (in inequality notation)?

Explanation:

Step1: Subtract 1 from both sides

To isolate the term with \( k \), we subtract 1 from both sides of the inequality \( 7 \geq 3k + 1 \). This gives us \( 7 - 1 \geq 3k + 1 - 1 \), which simplifies to \( 6 \geq 3k \).

Step2: Divide both sides by 3

Next, we divide both sides of the inequality \( 6 \geq 3k \) by 3 to solve for \( k \). So, \( \frac{6}{3} \geq \frac{3k}{3} \), which simplifies to \( 2 \geq k \) or equivalently \( k \leq 2 \).

Answer:

The solution to the inequality \( 7 \geq 3k + 1 \) is \( k \leq 2 \). For the number line graph, we draw a closed circle at 2 (since the inequality is "less than or equal to") and shade the line to the left of 2 to represent all values of \( k \) that satisfy the inequality.