To solve the expression:
[tex]\[ (-3x - 12) + (17 + 5x) \][/tex]
we proceed with the following steps:
1. Combine the like terms involving [tex]\( x \)[/tex]:
- The [tex]\( x \)[/tex]-terms are: [tex]\( -3x \)[/tex] and [tex]\( 5x \)[/tex].
- Add these terms together:
[tex]\[ -3x + 5x \][/tex]
2. Combine the constant terms:
- The constant terms are: [tex]\( -12 \)[/tex] and [tex]\( 17 \)[/tex].
- Add these terms together:
[tex]\[ -12 + 17 \][/tex]
3. Perform the arithmetic:
- For the [tex]\( x \)[/tex]-terms:
[tex]\[ -3x + 5x = 2x \][/tex]
- For the constant terms:
[tex]\[ -12 + 17 = 5 \][/tex]
4. Combine the simplified terms:
- Putting it all together:
[tex]\[ 2x + 5 \][/tex]
Thus, the expression using the fewest possible terms is:
[tex]\[ 2x + 5 \][/tex]
So, the correct answer is:
[tex]\[ 2 x + 5 \][/tex]
