Sure, let's solve the inequality step-by-step.
We start with the given inequality:
[tex]$(3 + 72) + (8 - 6) \leq (3 - 6) + (3 + 797)$[/tex]
Let's simplify each part of the inequality:
1. Simplify the left-hand side of the inequality:
[tex]$(3 + 72) + (8 - 6)$[/tex]
- First, compute [tex]\(3 + 72\)[/tex]:
[tex]$3 + 72 = 75$[/tex]
- Next, compute [tex]\(8 - 6\)[/tex]:
[tex]$8 - 6 = 2$[/tex]
- Now, add these results together:
[tex]$75 + 2 = 77$[/tex]
So the left-hand side simplifies to 77.
2. Simplify the right-hand side of the inequality:
[tex]$(3 - 6) + (3 + 797)$[/tex]
- First, compute [tex]\(3 - 6\)[/tex]:
[tex]$3 - 6 = -3$[/tex]
- Next, compute [tex]\(3 + 797\)[/tex]:
[tex]$3 + 797 = 800$[/tex]
- Now, add these results together:
[tex]$-3 + 800 = 797$[/tex]
So the right-hand side simplifies to 797.
Now, we rewrite the simplified inequality:
[tex]$77 \leq 797$[/tex]
We can see that [tex]\(77\)[/tex] is indeed less than or equal to [tex]\(797\)[/tex], so the inequality holds true.
Thus, the simplified answer is:
[tex]$(77, 797, \text{True})$[/tex]
This shows that the original inequality is correct.
