Answer :
Alright, let's solve the given expression step-by-step. The expression we are working with is:
[tex]\[ 4x - 3 \left[ x + 2(4 + x) \right] \][/tex]
### Part a) Simplified expression:
First, we need to simplify the expression inside the brackets.
1. Distribute the 2 inside the parentheses:
[tex]\[ x + 2(4 + x) = x + 2 \cdot 4 + 2 \cdot x = x + 8 + 2x \][/tex]
2. Combine like terms inside the brackets:
[tex]\[ x + 8 + 2x = 3x + 8 \][/tex]
Now substitute this back into the original expression:
[tex]\[ 4x - 3 (3x + 8) \][/tex]
3. Distribute the -3:
[tex]\[ 4x - 3 \cdot 3x - 3 \cdot 8 = 4x - 9x - 24 \][/tex]
4. Combine like terms:
[tex]\[ 4x - 9x - 24 = -5x - 24 \][/tex]
So the simplified expression is:
[tex]\[ -5x - 24 \][/tex]
### Part b) Evaluated expression:
Now we need to evaluate the simplified expression for [tex]\( x = 5 \)[/tex].
1. Substitute [tex]\( x = 5 \)[/tex] into the simplified expression:
[tex]\[ -5(5) - 24 \][/tex]
2. Perform the multiplication:
[tex]\[ -25 - 24 \][/tex]
3. Combine the terms:
[tex]\[ -25 - 24 = -49 \][/tex]
So the evaluated expression when [tex]\( x = 5 \)[/tex] is:
[tex]\[ -49 \][/tex]
### Summary:
a) Simplified expression: [tex]\(-5x - 24\)[/tex]
b) Evaluated expression: [tex]\(-49\)[/tex]
[tex]\[ 4x - 3 \left[ x + 2(4 + x) \right] \][/tex]
### Part a) Simplified expression:
First, we need to simplify the expression inside the brackets.
1. Distribute the 2 inside the parentheses:
[tex]\[ x + 2(4 + x) = x + 2 \cdot 4 + 2 \cdot x = x + 8 + 2x \][/tex]
2. Combine like terms inside the brackets:
[tex]\[ x + 8 + 2x = 3x + 8 \][/tex]
Now substitute this back into the original expression:
[tex]\[ 4x - 3 (3x + 8) \][/tex]
3. Distribute the -3:
[tex]\[ 4x - 3 \cdot 3x - 3 \cdot 8 = 4x - 9x - 24 \][/tex]
4. Combine like terms:
[tex]\[ 4x - 9x - 24 = -5x - 24 \][/tex]
So the simplified expression is:
[tex]\[ -5x - 24 \][/tex]
### Part b) Evaluated expression:
Now we need to evaluate the simplified expression for [tex]\( x = 5 \)[/tex].
1. Substitute [tex]\( x = 5 \)[/tex] into the simplified expression:
[tex]\[ -5(5) - 24 \][/tex]
2. Perform the multiplication:
[tex]\[ -25 - 24 \][/tex]
3. Combine the terms:
[tex]\[ -25 - 24 = -49 \][/tex]
So the evaluated expression when [tex]\( x = 5 \)[/tex] is:
[tex]\[ -49 \][/tex]
### Summary:
a) Simplified expression: [tex]\(-5x - 24\)[/tex]
b) Evaluated expression: [tex]\(-49\)[/tex]
