Question

solve the linear inequality for k and graph the answer in the number line. then write the solution in inequality notation.
4 ≥ k - 4
show your work here
hint: to add inequalities (<, >, ≤, ≥), type \less\ or \greater\

-15 -10 -5 0 5 10 15
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solution:

Explanation:

Step1: Add 4 to both sides

To solve for \( k \) in the inequality \( 4 \geq k - 4 \), we add 4 to both sides of the inequality. This is done to isolate the variable \( k \). The operation is \( 4 + 4 \geq k - 4 + 4 \).

Step2: Simplify both sides

Simplifying the left side \( 4 + 4 = 8 \) and the right side \( k - 4 + 4 = k \). So we get \( 8 \geq k \), which can also be written as \( k \leq 8 \).

Answer:

The solution to the inequality \( 4 \geq k - 4 \) is \( k \leq 8 \). To graph this on the number line, we would have a closed circle at 8 (since the inequality is "less than or equal to") and an arrow pointing to the left (indicating all values less than or equal to 8). In inequality notation, the solution is \( k \leq 8 \).