To simplify the expression [tex]\( 4(3x - 7) - 5(2x - 6) \)[/tex], we will follow these steps:
1. Distribute the constants inside the parentheses:
- Distribute the 4 to each term inside the first set of parentheses:
[tex]\[ 4 \times (3x - 7) = 4 \times 3x - 4 \times 7 \][/tex]
[tex]\[ = 12x - 28 \][/tex]
- Distribute the -5 to each term inside the second set of parentheses:
[tex]\[ -5 \times (2x - 6) = -5 \times 2x - (-5) \times 6 \][/tex]
[tex]\[ = -10x + 30 \][/tex]
2. Combine the distributed terms:
We now replace the original expression with the simplified parts we found:
[tex]\[ 4(3x - 7) - 5(2x - 6) \][/tex]
[tex]\[ = 12x - 28 - 10x + 30 \][/tex]
3. Combine like terms:
- Combine the [tex]\( x \)[/tex]-terms:
[tex]\[ 12x - 10x = 2x \][/tex]
- Combine the constant terms:
[tex]\[ -28 + 30 = 2 \][/tex]
4. Write the final simplified expression:
[tex]\[ 2x + 2 \][/tex]
So, the simplified form of the expression [tex]\( 4(3x - 7) - 5(2x - 6) \)[/tex] is [tex]\( 2x + 2 \)[/tex].
