Certainly! Let's rewrite the expression [tex]\(0.4(5y + 6z) + 7z - 0.1(8z + 10y)\)[/tex] in its simplest terms by breaking it down step by step.
1. Distribute the constants within the parentheses:
For the first part [tex]\(0.4(5y + 6z)\)[/tex]:
[tex]\[
0.4 \cdot 5y + 0.4 \cdot 6z = 2y + 2.4z
\][/tex]
For the second part [tex]\(-0.1(8z + 10y)\)[/tex]:
[tex]\[
-0.1 \cdot 8z - 0.1 \cdot 10y = -0.8z - y
\][/tex]
2. Substitute these results back into the original expression:
[tex]\[
2y + 2.4z + 7z - 0.8z - y
\][/tex]
3. Combine like terms:
Combine the [tex]\(y\)[/tex] terms:
[tex]\[
2y - y = y
\][/tex]
Combine the [tex]\(z\)[/tex] terms:
[tex]\[
2.4z + 7z - 0.8z = 8.6z
\][/tex]
4. Write the simplified expression:
Putting it all together, we get:
[tex]\[
y + 8.6z
\][/tex]
So, the simplest form of the expression [tex]\(0.4(5 y+6 z)+7 z-0.1(8 z+10 y)\)[/tex] is:
[tex]\[
y + 8.6z
\][/tex]
