Solve for r.

Question

5>
–
2r+3≥
–
11
Write your answer as a compound inequality with integers.

Answer 1

To solve the inequality

$$5-2r+3\ge -11,$$

first, combine like terms on the left side.

$$5+3=8,$$

so we have:

$$8-2r\ge -11.$$

Next, subtract 8 from both sides:

$$-2r\ge -11-8,$$

which simplifies to:

$$-2r\ge -19.$$

Now, divide by -2. Remember that when you divide or multiply by a negative number, you must reverse the inequality sign:

$$r\le \frac{-19}{-2}\Rightarrow r\le 9.5.$$

Since the problem asks for integers, we can conclude that:

$$r\le 9.$$

Since there is no lower boundary given in the original problem, let's assume $r$ can take any integer value less than or equal to 9. Thus, we can express this as:

$$r\in (-\mathrm{\infty },9].$$

Therefore, as a compound inequality for integers, the solution is:

$$r\le 9.$$

In terms of integers, the answer is:

$$r\in \dots ,-3,-2,-1,0,1,2,3,4,5,6,7,8,9.$$