Evaluate the Expressions 11 Worksheets - Free Printable

Problem Overview:

The task involves evaluating algebraic expressions using the given value \( y = 7 \). The expressions involve basic operations: addition, subtraction, multiplication, and the use of brackets. A dot (•) represents multiplication.

Solution Approach:

1. Substitute \( y = 7 \) into each expression.
2. Simplify the expressions step by step, following the order of operations (Parentheses/Brackets, Exponents, Multiplication and Division, Addition and Subtraction — PEMDAS/BODMAS).
3. Perform calculations carefully to ensure accuracy.

Step-by-Step Solutions:

#### Expression 1: \( 6 \cdot (3 \cdot y - 6) + 5 \cdot (7 + y) \)
- Substitute \( y = 7 \):
\[
6 \cdot (3 \cdot 7 - 6) + 5 \cdot (7 + 7)
\]
- Simplify inside the brackets:
\[
6 \cdot (21 - 6) + 5 \cdot 14
\]
\[
6 \cdot 15 + 5 \cdot 14
\]
- Perform the multiplications:
\[
90 + 70
\]
- Add the results:
\[
160
\]

Answer for Expression 1: \( \boxed{160} \)

#### Expression 2: \( 5 \cdot (7 \cdot y - 3) + 2 \cdot (8 + y) \)
- Substitute \( y = 7 \):
\[
5 \cdot (7 \cdot 7 - 3) + 2 \cdot (8 + 7)
\]
- Simplify inside the brackets:
\[
5 \cdot (49 - 3) + 2 \cdot 15
\]
\[
5 \cdot 46 + 2 \cdot 15
\]
- Perform the multiplications:
\[
230 + 30
\]
- Add the results:
\[
260
\]

Answer for Expression 2: \( \boxed{260} \)

#### Expression 3: \( 2 \cdot (8 \cdot y - 8) + 8 \cdot (6 + y) \)
- Substitute \( y = 7 \):
\[
2 \cdot (8 \cdot 7 - 8) + 8 \cdot (6 + 7)
\]
- Simplify inside the brackets:
\[
2 \cdot (56 - 8) + 8 \cdot 13
\]
\[
2 \cdot 48 + 8 \cdot 13
\]
- Perform the multiplications:
\[
96 + 104
\]
- Add the results:
\[
200
\]

Answer for Expression 3: \( \boxed{200} \)

#### Expression 4: \( (4 \cdot y + 8) + (2 \cdot y - 5) \)
- Substitute \( y = 7 \):
\[
(4 \cdot 7 + 8) + (2 \cdot 7 - 5)
\]
- Simplify inside the brackets:
\[
(28 + 8) + (14 - 5)
\]
\[
36 + 9
\]
- Add the results:
\[
45
\]

Answer for Expression 4: \( \boxed{45} \)

#### Expression 5: \( 4 \cdot (2 \cdot y - 2) + 8 \cdot (6 + y) \)
- Substitute \( y = 7 \):
\[
4 \cdot (2 \cdot 7 - 2) + 8 \cdot (6 + 7)
\]
- Simplify inside the brackets:
\[
4 \cdot (14 - 2) + 8 \cdot 13
\]
\[
4 \cdot 12 + 8 \cdot 13
\]
- Perform the multiplications:
\[
48 + 104
\]
- Add the results:
\[
152
\]

Answer for Expression 5: \( \boxed{152} \)

#### Expression 6: \( (3 \cdot y + 8) + (4 \cdot y - 2) \)
- Substitute \( y = 7 \):
\[
(3 \cdot 7 + 8) + (4 \cdot 7 - 2)
\]
- Simplify inside the brackets:
\[
(21 + 8) + (28 - 2)
\]
\[
29 + 26
\]
- Add the results:
\[
55
\]

Answer for Expression 6: \( \boxed{55} \)

#### Expression 7: \( (3 \cdot y + 6) + (7 \cdot y - 2) \)
- Substitute \( y = 7 \):
\[
(3 \cdot 7 + 6) + (7 \cdot 7 - 2)
\]
- Simplify inside the brackets:
\[
(21 + 6) + (49 - 2)
\]
\[
27 + 47
\]
- Add the results:
\[
74
\]

Answer for Expression 7: \( \boxed{74} \)

#### Expression 8: \( 5 \cdot (5 \cdot y - 3) + 6 \cdot (7 + y) \)
- Substitute \( y = 7 \):
\[
5 \cdot (5 \cdot 7 - 3) + 6 \cdot (7 + 7)
\]
- Simplify inside the brackets:
\[
5 \cdot (35 - 3) + 6 \cdot 14
\]
\[
5 \cdot 32 + 6 \cdot 14
\]
- Perform the multiplications:
\[
160 + 84
\]
- Add the results:
\[
244
\]

Answer for Expression 8: \( \boxed{244} \)

#### Expression 9: \( 5 \cdot (6 \cdot y - 6) + 3 \cdot (7 + y) \)
- Substitute \( y = 7 \):
\[
5 \cdot (6 \cdot 7 - 6) + 3 \cdot (7 + 7)
\]
- Simplify inside the brackets:
\[
5 \cdot (42 - 6) + 3 \cdot 14
\]
\[
5 \cdot 36 + 3 \cdot 14
\]
- Perform the multiplications:
\[
180 + 42
\]
- Add the results:
\[
222
\]

Answer for Expression 9: \( \boxed{222} \)

#### Expression 10: \( (8 \cdot y + 3) + (8 \cdot y - 4) \)
- Substitute \( y = 7 \):
\[
(8 \cdot 7 + 3) + (8 \cdot 7 - 4)
\]
- Simplify inside the brackets:
\[
(56 + 3) + (56 - 4)
\]
\[
59 + 52
\]
- Add the results:
\[
111
\]

Answer for Expression 10: \( \boxed{111} \)

Final Answers:

\[
\boxed{160, 260, 200, 45, 152, 55, 74, 244, 222, 111}
\]