negative 5 r plus 6 is less than or equal to negative 5 times left parenthesis r plus 2 right parenthesis
Starting with the given equation:
-5r + 6 ≤ -5(r + 2)
Let's simplify this:
-5r + 6 ≤ -5r - 10
Next, let's isolate the variable by getting rid of the negative sign:
5r + -5r + 6 ≤ -5r + -5r - 10
Combining like terms, we have:
6 ≤ -10
This equation is not true. Therefore, there is no solution for this inequality.
To solve the inequality, let's simplify the expression on both sides step-by-step:
1. Start with the given inequality: -5r + 6 ≤ -5(r + 2).
2. Distribute the -5 on the right side: -5r + 6 ≤ -5r - 10.
3. Combine like terms on both sides: -5r + 6 ≤ -5r - 10 + 5r.
4. Simplify: -5r + 6 ≤ -10.
5. Move all terms to one side of the inequality: -5r + 5r + 6 ≤ -10 + 5r.
6. Simplify: 6 ≤ -10 + 5r.
7. Combine like terms: 6 ≤ 5r - 10.
8. Add 10 to both sides: 6 + 10 ≤ 5r - 10 + 10.
9. Simplify: 16 ≤ 5r.
10. Divide both sides by 5, remembering to reverse the inequality when dividing by a negative number: 16/5 ≥ 5r/5.
11. Simplify: 16/5 ≥ r.
12. The final solution is: r ≤ 16/5 or r ≤ 3.2.
So the values of r that satisfy the inequality are any values less than or equal to 3.2.