Of course! Let's solve the expression step-by-step.
We start with the expression:
[tex]\[
5(1 - 2x) - 3(x + 6)
\][/tex]
Step 1: Distribute the 5 within the first parentheses.
[tex]\[
5 \cdot 1 - 5 \cdot 2x
\][/tex]
This gives us:
[tex]\[
5 - 10x
\][/tex]
Step 2: Distribute the [tex]\(-3\)[/tex] within the second parentheses.
[tex]\[
-3 \cdot x - 3 \cdot 6
\][/tex]
This gives us:
[tex]\[
-3x - 18
\][/tex]
Step 3: Combine the results from both distributions.
We have:
[tex]\[
5 - 10x - 3x - 18
\][/tex]
Step 4: Simplify by combining like terms.
- Combine the constant terms: [tex]\(5\)[/tex] and [tex]\(-18\)[/tex]:
[tex]\[
5 - 18 = -13
\][/tex]
- Combine the [tex]\(x\)[/tex]-terms: [tex]\(-10x\)[/tex] and [tex]\(-3x\)[/tex]:
[tex]\[
-10x - 3x = -13x
\][/tex]
Thus, the simplified form of the expression is:
[tex]\[
-13 - 13x
\][/tex]
So the expanded and simplified form of the original expression [tex]\(5(1 - 2x) - 3(x + 6)\)[/tex] is:
[tex]\[
-13 - 13x
\][/tex]
