Sure, let's simplify the expression step by step.
Given the expression:
[tex]\[
-4(9 + 3x) - 4(x - 2)
\][/tex]
1. Distribute -4 in both terms:
- For the first term [tex]\( -4(9 + 3x) \)[/tex]:
[tex]\[
-4 \times 9 + (-4) \times 3x = -36 - 12x
\][/tex]
- For the second term [tex]\( -4(x - 2) \)[/tex]:
[tex]\[
-4 \times x + (-4) \times (-2) = -4x + 8
\][/tex]
2. Combine the results:
- Combine the expressions [tex]\(-36 - 12x\)[/tex] and [tex]\(-4x + 8\)[/tex]:
[tex]\[
-36 - 12x - 4x + 8
\][/tex]
3. Simplify by combining like terms:
- Combine the [tex]\( x \)[/tex] terms ([tex]\( -12x \)[/tex] and [tex]\( -4x \)[/tex]):
[tex]\[
-12x - 4x = -16x
\][/tex]
- Combine the constant terms ([tex]\( -36 \)[/tex] and [tex]\( 8 \)[/tex]):
[tex]\[
-36 + 8 = -28
\][/tex]
Putting it all together, the simplified expression is:
[tex]\[
-16x - 28
\][/tex]
So, the final answer is:
[tex]\[
-4(9 + 3x) - 4(x - 2) = -16x - 28
\][/tex]
