Question

solve the inequality. graph the solution on a number line and represent the solution in interval - notation when possible. 6≤4 - r. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the solution is r≤ - 2 (type an inequality. simplify your answer.) b. the solution is all real numbers. c. there is no solution. choose the correct graph of the inequality.

Explanation:

Step1: Solve the inequality

Given $6\leq4 - r$. Subtract 4 from both sides: $6 - 4\leq4 - r-4$, which simplifies to $2\leq - r$. Multiply both sides by - 1 and reverse the inequality sign (since multiplying by a negative number), we get $r\leq - 2$.

Step2: Analyze the graph

The solution $r\leq - 2$ is represented on a number - line with a closed circle at - 2 (because the inequality includes equality, $\leq$) and an arrow pointing to the left.

Answer:

A. The solution is $r\leq - 2$; the correct graph has a closed circle at - 2 and an arrow pointing left.