Solve for
y
y
.
−
6
y
+
5
(
−
4
y
−
7
)
=
−
1
−
3
(
−
8
−
y
)
-
6
y
+
5
(
-
4
y
-
7
)
=
-
1
-
3
(
-
8
-
y
)

We are given the equation:

\[
-6y + 5(-4y - 7) = -1 - 3(-8 - y)
\]

### Step 1: Expand both sides

Expand the terms on both sides of the equation:

\[
-6y + 5(-4y - 7) = -1 - 3(-8 - y)
\]

Distribute the \(5\) and the \(-3\):

\[
-6y + 5(-4y) + 5(-7) = -1 - 3(-8) - 3(-y)
\]

This becomes:

\[
-6y - 20y - 35 = -1 + 24 + 3y
\]

### Step 2: Combine like terms

Simplify both sides:

\[
-26y - 35 = 23 + 3y
\]

### Step 3: Move all terms involving \(y\) to one side

Add \(26y\) to both sides:

\[
-35 = 23 + 29y
\]

### Step 4: Move constant terms to the other side

Subtract \(23\) from both sides:

\[
-35 - 23 = 29y
\]

\[
-58 = 29y
\]

### Step 5: Solve for \(y\)

Divide both sides by \(29\):

\[
y = \frac{-58}{29} = -2
\]

### Final Answer:

\[
y = -2
\]

Would you like further details or have any questions?

---

Here are five questions based on this:

1. How do you distribute terms inside parentheses when solving equations?
2. What strategies help simplify equations with multiple variables?
3. How do you combine like terms effectively?
4. Why do we move terms with variables to one side of the equation?
5. What is the importance of checking your solution by substituting back into the original equation?

**Tip:** Always check your final solution by substituting it back into the original equation to verify its correctness.

Solve for y: -6y + 5(-4y - 7) = -1 - 3(-8 - y)

Step-by-step solution to solve the linear equation -6y + 5(-4y - 7) = -1 - 3(-8 - y). This example covers key algebraic concepts, including distributing terms, combining like terms, and solving for variables. Suitable for students in Grades 8-10.

Math Problem Statement

Solve for y y . − 6 y + 5 ( − 4 y − 7 )

− 1 − 3 ( − 8 − y )

6 y + 5 (

4 y

7 )

1

3 (

8

Solution

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