Certainly! Let's simplify each expression step-by-step:
### (a) Simplifying [tex]\( x + 7 + 4(x - 5) \)[/tex]
1. Distribute the 4 inside the parentheses:
[tex]\[
x + 7 + 4(x - 5) = x + 7 + 4x - 20
\][/tex]
2. Combine like terms:
- Combine the [tex]\( x \)[/tex] terms: [tex]\( x + 4x \)[/tex]
- Combine the constants: [tex]\( 7 - 20 \)[/tex]
So, it becomes:
[tex]\[
x + 4x + 7 - 20 = 5x - 13
\][/tex]
Thus, the simplified form of [tex]\( x + 7 + 4(x - 5) \)[/tex] is:
[tex]\[
5x - 13
\][/tex]
### (b) Simplifying [tex]\( 6x + 5(x - 2) \)[/tex]
1. Distribute the 5 inside the parentheses:
[tex]\[
6x + 5(x - 2) = 6x + 5x - 10
\][/tex]
2. Combine like terms:
- Combine the [tex]\( x \)[/tex] terms: [tex]\( 6x + 5x \)[/tex]
- Then add the constant term: [tex]\(-10\)[/tex]
So, it becomes:
[tex]\[
6x + 5x - 10 = 11x - 10
\][/tex]
Thus, the simplified form of [tex]\( 6x + 5(x - 2) \)[/tex] is:
[tex]\[
11x - 10
\][/tex]
So, the final simplified expressions are:
[tex]\[
\text{(a)} \quad 5x - 13
\][/tex]
[tex]\[
\text{(b)} \quad 11x - 10
\][/tex]
