Question

solve the inequality and graph the solution. -(k - 10) - 1 > 1 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.

Explanation:

Step1: Simplify the left - hand side

First, distribute the negative sign in $-(k - 10)$: $-k+10 - 1>1$. Then combine like - terms: $-k + 9>1$.

Step2: Isolate the variable term

Subtract 9 from both sides of the inequality: $-k+9 - 9>1 - 9$, which simplifies to $-k>-8$.

Step3: Solve for k

Multiply both sides of the inequality by - 1. Remember to reverse the inequality sign when multiplying by a negative number. So, $(-1)\times(-k)<(-1)\times(-8)$, which gives $k < 8$.

Answer:

The solution of the inequality is $k < 8$. On the number - line, we plot an open circle at 8 (since the inequality is strict, $k$ cannot equal 8) and draw a ray to the left of 8.