Sure, let's simplify the given expression step by step:
We start with the expression:
[tex]\[ 4(1 - 3x) + 7x - 8 \][/tex]
1. Distribute the 4 in the first term:
Here, you need to apply the distributive property, multiplying 4 by each term inside the parentheses:
[tex]\[ 4 \cdot 1 - 4 \cdot 3x = 4 - 12x \][/tex]
2. Substitute the distributed values back into the expression:
[tex]\[ 4 - 12x + 7x - 8 \][/tex]
3. Combine like terms:
- Combine the constant terms [tex]\( 4 \)[/tex] and [tex]\( -8 \)[/tex]:
[tex]\[ 4 - 8 = -4 \][/tex]
- Combine the [tex]\( x \)[/tex]-terms [tex]\( -12x \)[/tex] and [tex]\( +7x \)[/tex]:
[tex]\[ -12x + 7x = -5x \][/tex]
4. Write the simplified expression:
[tex]\[ -4 - 5x \][/tex]
Therefore, the simplified expression is:
[tex]\[ -5x - 4 \][/tex]
