Question

solve the linear inequality for k and graph the answer in the number line. then write the solution in inequality notation.
1 > k - 1
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 1 to both sides

To solve for \( k \) in the inequality \( 1 > k - 1 \), we add 1 to both sides of the inequality. This is done to isolate the variable \( k \). The operation is \( 1 + 1 > k - 1 + 1 \).

Step2: Simplify both sides

Simplifying the left - hand side \( 1+1 = 2 \), and on the right - hand side \( k-1 + 1=k \). So we get \( 2>k \), which can also be written as \( k < 2 \).

Answer:

The solution to the inequality \( 1>k - 1 \) is \( k < 2 \). To graph this on the number line, we would have an open circle at \( k = 2 \) (since the inequality is strict, \( k
eq2 \)) and a line pointing to the left (towards values less than 2) to represent all values of \( k \) that satisfy the inequality. The inequality notation for the solution is \( k < 2 \).