To simplify the expression [tex]\(4(x+3)-5(x-2)\)[/tex], let's go through it step by step:
1. Distribute the constants inside the parentheses:
- Distribute the 4 in [tex]\(4(x + 3)\)[/tex]
[tex]\[
4 \cdot x + 4 \cdot 3 = 4x + 12
\][/tex]
- Distribute the -5 in [tex]\(-5(x - 2)\)[/tex]
[tex]\[
-5 \cdot x - 5 \cdot (-2) = -5x + 10
\][/tex]
2. Combine the distributed parts:
Now we have:
[tex]\[
4x + 12 - 5x + 10
\][/tex]
3. Group like terms:
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[
4x - 5x = -x
\][/tex]
- Combine the constant terms:
[tex]\[
12 + 10 = 22
\][/tex]
4. Write the simplified expression:
Putting it all together, we get:
[tex]\[
-x + 22
\][/tex]
So, the simplified expression is [tex]\(-x + 22\)[/tex].
