Let's solve the equation step by step:

The given equation is:

\[
-4(y - 2) + 6(3y + 1) = 10
\]

### Step 1: Distribute the numbers outside the parentheses
Distribute \(-4\) across \((y - 2)\) and \(6\) across \((3y + 1)\):

\[
-4y + 8 + 18y + 6 = 10
\]

### Step 2: Combine like terms
Combine the \(y\) terms and the constant terms on the left side:

\[
(-4y + 18y) + (8 + 6) = 10
\]

\[
14y + 14 = 10
\]

### Step 3: Isolate the variable term
Subtract 14 from both sides to isolate the term with \(y\):

\[
14y = 10 - 14
\]

\[
14y = -4
\]

### Step 4: Solve for \(y\)
Divide both sides by 14 to solve for \(y\):

\[
y = \frac{-4}{14}
\]

Simplify the fraction:

\[
y = \frac{-2}{7}
\]

### Final Answer:
\[
y = -\frac{2}{7}
\]

Would you like more details or have any questions?

Here are 5 related questions to practice:

1. Solve: \(3(2y - 5) = 2(4y + 1)\)
2. Solve: \(5y - 3(2y + 4) = 7\)
3. Solve: \(4(2y + 3) - 10 = 2y + 14\)
4. Solve: \(-6(y - 1) + 4(2y + 5) = 8\)
5. Solve: \(7y - 2(y + 4) = 3\)

**Tip:** Always simplify expressions as much as possible before isolating the variable. This reduces the chances of mistakes.

Learn how to solve the equation -4(y-2) + 6(3y+1) = 10 with a detailed step-by-step solution. This problem covers algebraic concepts such as distributing numbers across parentheses, combining like terms, and isolating the variable. Suitable for students in Grades 7-9.

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