To find the sum of the given expressions, let's break down the problem and combine like terms step-by-step.
Start with the given expression:
[tex]$
(-7b + 8c) - (12a + 14) + (5a + 5b)
$[/tex]
Let's break it down:
1. Distribute the minus sign through the second group:
[tex]$
(-7b + 8c) - 12a - 14 + (5a + 5b)
$[/tex]
2. Now, group all the [tex]\(a\)[/tex]-terms, [tex]\(b\)[/tex]-terms, and [tex]\(c\)[/tex]-terms together:
- Combine the [tex]\(a\)[/tex]-terms:
[tex]$ -12a + 5a = -7a $[/tex]
- Combine the [tex]\(b\)[/tex]-terms:
[tex]$ -7b + 5b = -2b $[/tex]
- The [tex]\(c\)[/tex]-term remains unchanged:
[tex]$ 8c $[/tex]
3. Combine the constant terms:
- Combine the constants:
[tex]$ -14 $[/tex]
Thus, after combining like terms, the expression simplifies to:
[tex]$
-7a - 2b + 8c - 14
$[/tex]
Therefore, the simplified sum of the given expression is:
[tex]$
-7a - 2b + 8c - 14
$[/tex]
