To find the sum of the given expressions [tex]\((-7b + 8c) - (12a + 14) + (5a + 5)\)[/tex], let's follow these step-by-step instructions:
1. Distribute the negative sign in the second term:
[tex]\[- (12a + 14)\][/tex] becomes [tex]\(-12a - 14\)[/tex].
2. Write each term separately:
[tex]\[
\text{First expression: } -7b + 8c \\
\text{Second expression: } -12a - 14 \\
\text{Third expression: } 5a + 5
\][/tex]
3. Combine all the expressions into one:
[tex]\[
-7b + 8c - 12a - 14 + 5a + 5
\][/tex]
4. Group like terms together:
[tex]\[
-12a + 5a - 7b + 8c - 14 + 5
\][/tex]
5. Simplify the like terms:
[tex]\[
-12a + 5a = -7a \\
-14 + 5 = -9
\][/tex]
6. Combine all the simplified terms:
[tex]\[
-7a - 7b + 8c - 9
\][/tex]
So, the simplified expression is:
[tex]\[
-7a - 7b + 8c - 9
\][/tex]
Since none of the answer choices matches this exactly, it appears the given choices might have typographical errors. The correct simplified expression is:
[tex]\[
-7a - 7b + 8c - 9
\][/tex]
