Question

Solve for r. Your answer must be simplified. r − 15 ≤ − 6

Answer 1

r ≤ 9 .Adding 15 to both sides of
`\(r - 15 \leq -6\)` isolates
`\(r\)`, yielding
`\(r \leq 9\)`, indicating all
`\(r\)` values less than or equal to 9 satisfy the inequality.

Step-by-step explanation:

To solve the inequality
`\(r - 15 \leq -6\)`, add 15 to both sides to isolate the variable. This gives
`\(r \leq 9\)`. In the original inequality, subtracting 15 from both sides brings
`\(r\)` to one side and simplifies the inequality, resulting in
`\(r \leq 9\)\\`. Therefore, any value of
`\(r\)` that is less than or equal to 9 satisfies the given inequality.

In the process of solving, when adding 15 to both sides, it cancels out the -15 on the left side of the inequality, leaving
`\(r\)`by itself. This manipulation maintains the inequality's direction, giving
`\(r \leq 9\)`as the solution. The interpretation is that any real number less than or equal to 9 is a valid solution to the original inequality.

Graphically, this solution represents all values of
`\(r\)` to the left of and including 9 on the number line. The solution set is inclusive of 9, meaning that 9 is also a valid solution.