To simplify the expression [tex]\( 19w - 2(6w + 3) \)[/tex], we'll follow the steps of removing the parentheses through distribution and then combining like terms.
1. Distribute the [tex]\(-2\)[/tex]:
When we distribute [tex]\(-2\)[/tex] across the terms inside the parentheses, each term inside the parentheses gets multiplied by [tex]\(-2\)[/tex].
[tex]\[
-2(6w + 3) = (-2) \cdot 6w + (-2) \cdot 3 = -12w - 6
\][/tex]
2. Rewrite the expression with the distributed terms:
Now, we replace the original parenthetical expression with the results of our distribution.
[tex]\[
19w - 2(6w + 3) = 19w - 12w - 6
\][/tex]
3. Combine like terms:
We combine the terms that have the variable [tex]\(w\)[/tex].
[tex]\[
19w - 12w = 7w
\][/tex]
4. Simplified expression:
Now we put together all the simplified components.
[tex]\[
7w - 6
\][/tex]
Therefore, the simplified form of the expression [tex]\(19w - 2(6w + 3)\)[/tex] is:
[tex]\[
7w - 6
\][/tex]
