solve this using solving equatioj method: −3(y+4)+2(5y−2)=8

To solve the equation \(-3(y + 4) + 2(5y - 2) = 8\), let's follow the steps of solving equations methodically:

### Step 1: Distribute the constants
Distribute \(-3\) across \((y + 4)\) and \(2\) across \((5y - 2)\):

\[
-3(y + 4) = -3y - 12
\]
\[
2(5y - 2) = 10y - 4
\]

Now, the equation becomes:

\[
-3y - 12 + 10y - 4 = 8
\]

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

\[
(-3y + 10y) + (-12 - 4) = 8
\]
\[
7y - 16 = 8
\]

### Step 3: Solve for \(y\)
Add 16 to both sides of the equation to isolate the term with \(y\):

\[
7y - 16 + 16 = 8 + 16
\]
\[
7y = 24
\]

Now, divide both sides by 7 to solve for \(y\):

\[
y = \frac{24}{7}
\]

### Final Answer:
\[
y = \frac{24}{7}
\]

Would you like a deeper explanation or have any questions? 

Here are some related questions:
1. How do you check your solution for an equation?
2. What happens if an equation has no solution?
3. How can you solve equations with fractions?
4. What is the method of substitution for solving systems of equations?
5. Can you solve equations graphically?

**Tip:** Always double-check your work by plugging your solution back into the original equation to verify correctness.

Learn how to solve the equation -3(y + 4) + 2(5y - 2) = 8 with a detailed step-by-step method. This problem covers key algebraic concepts, including equations, distributive property, and combining like terms. Suitable for high school students.

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