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Simplify and evaluate the expression:

[tex]\[ 4x - 3[x + 2(4 + x)] \][/tex]

a) Simplified expression: [tex]$\square$[/tex]

b) Evaluated expression for [tex]\( x = \square \)[/tex]: [tex]$\square$[/tex]

Sagot :

GinnyAnsweridn
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]
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