Question

students will red each expression simplify, and check that their final expression makes sense computed to the c...

q	expression	work space	simplified answer
2	$(6y - 3) + 4(2y + 7)$
3	$5(y + 8) - (3y - 2)$
4	$2(3y - 4) + 3(5y + 1)$
5	$7y + 6(2y - 3) - 4$
6	$4(y + 9) - 2(3y - 1)$
7	$(5y + 6) + 3(4y - 2)$
8	$8 - 3(2y - 7) + y$
9	$6(y - 5) + (4y + 3)$
10	$2(5y + 4) - 3(y - 6)$

Explanation:

To solve the expression \( 3(4y + 1) - 2(y - 5) \), we follow these steps:

Step 1: Distribute the coefficients

First, we distribute the 3 into \( (4y + 1) \) and the -2 into \( (y - 5) \):
\[
3(4y + 1) = 3 \cdot 4y + 3 \cdot 1 = 12y + 3
\]
\[
-2(y - 5) = -2 \cdot y + (-2) \cdot (-5) = -2y + 10
\]

Step 2: Combine the distributed terms

Now we substitute these back into the original expression:
\[
12y + 3 - 2y + 10
\]

Step 3: Combine like terms

We combine the \( y \)-terms and the constant terms:
\[
(12y - 2y) + (3 + 10) = 10y + 13
\]

Final Answer

The simplified form of \( 3(4y + 1) - 2(y - 5) \) is \(\boxed{10y + 13}\).

Answer:

To solve the expression \( 3(4y + 1) - 2(y - 5) \), we follow these steps:

Step 1: Distribute the coefficients

First, we distribute the 3 into \( (4y + 1) \) and the -2 into \( (y - 5) \):
\[
3(4y + 1) = 3 \cdot 4y + 3 \cdot 1 = 12y + 3
\]
\[
-2(y - 5) = -2 \cdot y + (-2) \cdot (-5) = -2y + 10
\]

Step 2: Combine the distributed terms

Now we substitute these back into the original expression:
\[
12y + 3 - 2y + 10
\]

Step 3: Combine like terms

We combine the \( y \)-terms and the constant terms:
\[
(12y - 2y) + (3 + 10) = 10y + 13
\]

Final Answer

The simplified form of \( 3(4y + 1) - 2(y - 5) \) is \(\boxed{10y + 13}\).