https://file.aiquickdraw.com/mathbot/file/1727043956132o2snp5ev.jpg

Let's solve the equation from the image:

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

### Step 1: Distribute the \(-3\) on the right-hand side.
\[
5y - 10 = -3 \cdot 4 + (-3) \cdot (-2x)
\]
\[
5y - 10 = -12 + 6x
\]

### Step 2: Move all constants to one side of the equation.
Add 10 to both sides:
\[
5y = 6x - 12 + 10
\]
\[
5y = 6x - 2
\]

### Step 3: Solve for \(y\).
Divide both sides by 5:
\[
y = \frac{6x - 2}{5}
\]

Thus, the solution is:
\[
y = \frac{6x - 2}{5}
\]

Would you like any further details on this solution?

### 5 Related Questions:
1. How would you graph the equation \(y = \frac{6x - 2}{5}\)?
2. What happens if you set \(x = 0\) in the equation \(y = \frac{6x - 2}{5}\)?
3. How can you check if a pair \((x, y)\) satisfies the equation \(y = \frac{6x - 2}{5}\)?
4. What is the slope and y-intercept of the equation \(y = \frac{6x - 2}{5}\)?
5. How would the equation change if the right side was multiplied by a different constant?

### Tip:
When distributing, always pay attention to negative signs to avoid mistakes, especially with subtraction.

Discover how to solve the linear equation 5y - 10 = -3(4 - 2x) with a step-by-step guide. This problem involves key algebraic concepts such as distribution and solving for variables. Suitable for students in Grades 8-10.

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