To simplify the expression [tex]\(4(1 - 2b) + 7b - 10\)[/tex], we will follow a series of steps involving distribution and combining like terms. Here's the step-by-step solution:
1. Distribute the 4 across the terms inside the parentheses:
[tex]\[
4 \cdot 1 - 4 \cdot 2b
\][/tex]
This simplifies to:
[tex]\[
4 - 8b
\][/tex]
2. Rewrite the original expression with the distributed terms:
[tex]\[
4 - 8b + 7b - 10
\][/tex]
3. Combine like terms:
- Combine the constant terms: [tex]\(4 - 10\)[/tex]:
[tex]\[
4 - 10 = -6
\][/tex]
- Combine the [tex]\(b\)[/tex]-terms: [tex]\(-8b + 7b\)[/tex]:
[tex]\[
-8b + 7b = -b
\][/tex]
4. Write the simplified expression:
[tex]\[
-6 - b
\][/tex]
Thus, the simplified expression is:
[tex]\[
-6 - b
\][/tex]
