To simplify the expression [tex]\( 6(y+3) \div 2 \cdot 3 + 8 \)[/tex], we'll go through the process step by step:
1. Simplify Inside the Parentheses:
Start with the expression inside the parentheses:
[tex]\[
y + 3
\][/tex]
2. Multiply the Expression by 6:
Next, we multiply the expression [tex]\( y + 3 \)[/tex] by 6:
[tex]\[
6(y + 3)
\][/tex]
3. Divide by 2:
Now, divide the resulting expression by 2:
[tex]\[
\frac{6(y + 3)}{2}
\][/tex]
This simplifies to:
[tex]\[
3(y + 3)
\][/tex]
4. Multiply by 3:
Multiply the expression [tex]\( 3(y + 3) \)[/tex] by 3:
[tex]\[
3(y + 3) \cdot 3
\][/tex]
This gives:
[tex]\[
9(y + 3)
\][/tex]
5. Distribute the 9:
Distribute the 9 into the parenthesis:
[tex]\[
9y + 27
\][/tex]
6. Add 8:
Finally, add 8 to the expression:
[tex]\[
9y + 27 + 8
\][/tex]
7. Combine Like Terms:
Combine the constants:
[tex]\[
9y + 35
\][/tex]
So, the simplified form of the expression [tex]\( 6(y+3) \div 2 \cdot 3 + 8 \)[/tex] is:
[tex]\[
9y + 35
\][/tex]
