To expand and simplify the given expression, [tex]\( 5(2x - 1) + 2(3x - 6) \)[/tex], follow these steps:
1. Distribute the constants:
- For the first term: [tex]\( 5(2x - 1) \)[/tex]:
- Multiply 5 with [tex]\( 2x \)[/tex]: [tex]\( 5 \cdot 2x = 10x \)[/tex].
- Multiply 5 with -1: [tex]\( 5 \cdot (-1) = -5 \)[/tex].
- So, [tex]\( 5(2x - 1) = 10x - 5 \)[/tex].
- For the second term: [tex]\( 2(3x - 6) \)[/tex]:
- Multiply 2 with [tex]\( 3x \)[/tex]: [tex]\( 2 \cdot 3x = 6x \)[/tex].
- Multiply 2 with -6: [tex]\( 2 \cdot (-6) = -12 \)[/tex].
- So, [tex]\( 2(3x - 6) = 6x - 12 \)[/tex].
2. Combine the expanded terms:
- Now, add the results from the first and the second term:
- [tex]\( 10x - 5 + 6x - 12 \)[/tex].
3. Combine like terms:
- Combine the [tex]\( x \)[/tex]-terms: [tex]\( 10x + 6x = 16x \)[/tex].
- Combine the constant terms: [tex]\( -5 - 12 = -17 \)[/tex].
Therefore, the expanded and simplified form of [tex]\( 5(2x - 1) + 2(3x - 6) \)[/tex] is:
[tex]\[ 16x - 17 \][/tex]
I made separate notes on each step to ensure clarity.
