Answer :
Let's solve the inequality step by step:
We have the inequality: [tex]\(-10r - 3 \geq 10r + 6\)[/tex].
1. First, let's get all terms involving [tex]\(r\)[/tex] on one side of the inequality. This means we should move the [tex]\(10r\)[/tex] from the right side to the left side. To do this, subtract [tex]\(10r\)[/tex] from both sides:
[tex]\(-10r - 3 - 10r \geq 6\)[/tex].
This simplifies to:
[tex]\(-20r - 3 \geq 6\)[/tex].
2. Next, we need to move the constant term (-3) on the left side over to the right side. Add 3 to both sides:
[tex]\(-20r \geq 6 + 3\)[/tex].
This results in:
[tex]\(-20r \geq 9\)[/tex].
3. Now, solve for [tex]\(r\)[/tex] by dividing both sides by [tex]\(-20\)[/tex]. Remember, when you divide or multiply both sides of an inequality by a negative number, you must flip the inequality sign:
[tex]\(r \leq \frac{9}{-20}\)[/tex].
Simplifying the right side, we get:
[tex]\(r \leq -0.45\)[/tex].
So, the solution to the inequality is [tex]\(r \leq -0.45\)[/tex].
We have the inequality: [tex]\(-10r - 3 \geq 10r + 6\)[/tex].
1. First, let's get all terms involving [tex]\(r\)[/tex] on one side of the inequality. This means we should move the [tex]\(10r\)[/tex] from the right side to the left side. To do this, subtract [tex]\(10r\)[/tex] from both sides:
[tex]\(-10r - 3 - 10r \geq 6\)[/tex].
This simplifies to:
[tex]\(-20r - 3 \geq 6\)[/tex].
2. Next, we need to move the constant term (-3) on the left side over to the right side. Add 3 to both sides:
[tex]\(-20r \geq 6 + 3\)[/tex].
This results in:
[tex]\(-20r \geq 9\)[/tex].
3. Now, solve for [tex]\(r\)[/tex] by dividing both sides by [tex]\(-20\)[/tex]. Remember, when you divide or multiply both sides of an inequality by a negative number, you must flip the inequality sign:
[tex]\(r \leq \frac{9}{-20}\)[/tex].
Simplifying the right side, we get:
[tex]\(r \leq -0.45\)[/tex].
So, the solution to the inequality is [tex]\(r \leq -0.45\)[/tex].
