Answer :
Let's solve the inequality step-by-step:
We are given the inequality:
[tex]\[
-10r - 3 \geq 10r + 6
\][/tex]
Step 1: Move all terms involving [tex]\( r \)[/tex] to one side.
Subtract [tex]\( 10r \)[/tex] from both sides:
[tex]\[
-10r - 10r - 3 \geq 10r - 10r + 6
\][/tex]
This simplifies to:
[tex]\[
-20r - 3 \geq 6
\][/tex]
Step 2: Move the constant term to the other side.
Add 3 to both sides:
[tex]\[
-20r - 3 + 3 \geq 6 + 3
\][/tex]
This simplifies to:
[tex]\[
-20r \geq 9
\][/tex]
Step 3: Solve for [tex]\( r \)[/tex] by dividing both sides by -20.
Remember that when you divide or multiply both sides of an inequality by a negative number, the inequality sign reverses:
[tex]\[
r \leq \frac{9}{-20}
\][/tex]
Final Answer:
The solution for the inequality is:
[tex]\[
r \leq -0.45
\][/tex]
We are given the inequality:
[tex]\[
-10r - 3 \geq 10r + 6
\][/tex]
Step 1: Move all terms involving [tex]\( r \)[/tex] to one side.
Subtract [tex]\( 10r \)[/tex] from both sides:
[tex]\[
-10r - 10r - 3 \geq 10r - 10r + 6
\][/tex]
This simplifies to:
[tex]\[
-20r - 3 \geq 6
\][/tex]
Step 2: Move the constant term to the other side.
Add 3 to both sides:
[tex]\[
-20r - 3 + 3 \geq 6 + 3
\][/tex]
This simplifies to:
[tex]\[
-20r \geq 9
\][/tex]
Step 3: Solve for [tex]\( r \)[/tex] by dividing both sides by -20.
Remember that when you divide or multiply both sides of an inequality by a negative number, the inequality sign reverses:
[tex]\[
r \leq \frac{9}{-20}
\][/tex]
Final Answer:
The solution for the inequality is:
[tex]\[
r \leq -0.45
\][/tex]
