Sure! Let’s break down the expression [tex]\( -0.4(-6g - 9h) - 2h - 0.2(-5h + 3g) \)[/tex] step-by-step and simplify it to its simplest terms.
1. Distribute the constants:
- Distribute [tex]\(-0.4\)[/tex] to each term inside the first parentheses:
[tex]\[
-0.4(-6g) + -0.4(-9h) = 2.4g + 3.6h
\][/tex]
- Distribute [tex]\(-0.2\)[/tex] to each term inside the second parentheses:
[tex]\[
-0.2(-5h) + -0.2(3g) = 1h - 0.6g
\][/tex]
2. Combine all the terms together:
[tex]\[
2.4g + 3.6h - 2h + 1h - 0.6g
\][/tex]
3. Group like terms:
- Combine the [tex]\( g \)[/tex] terms:
[tex]\[
2.4g - 0.6g = 1.8g
\][/tex]
- Combine the [tex]\( h \)[/tex] terms:
[tex]\[
3.6h - 2h + 1h = 2.6h
\][/tex]
4. Write the final simplified expression:
[tex]\[
1.8g + 2.6h
\][/tex]
Therefore, the expression [tex]\( -0.4(-6g - 9h) - 2h - 0.2(-5h + 3g) \)[/tex] simplifies to [tex]\( \boxed{1.8g + 2.6h} \)[/tex].
