Let's solve the equation \( 5 \times (2a - 1) - 3a + 5 = 2 \times (2a + 6) \).

### Step 1: Distribute the constants
First, distribute the constants \(5\) and \(2\) through the parentheses on both sides:

\[
5 \times (2a - 1) = 10a - 5
\]
\[
2 \times (2a + 6) = 4a + 12
\]

Now, substitute these into the original equation:

\[
10a - 5 - 3a + 5 = 4a + 12
\]

### Step 2: Combine like terms
Next, combine like terms on the left side:

\[
(10a - 3a) + (-5 + 5) = 7a + 0 = 7a
\]

So, the equation simplifies to:

\[
7a = 4a + 12
\]

### Step 3: Isolate the variable
Now, subtract \(4a\) from both sides to isolate \(a\):

\[
7a - 4a = 12
\]
\[
3a = 12
\]

### Step 4: Solve for \(a\)
Finally, divide both sides by 3:

\[
a = \frac{12}{3} = 4
\]

### Solution
The solution is \( a = 4 \).

Would you like details on any step or have any questions? Here are some related questions to explore:

1. How do you solve equations involving variables on both sides?
2. What are some strategies for distributing constants in equations?
3. How can you check if your solution to an equation is correct?
4. What is the significance of isolating the variable in an equation?
5. How would this equation change if there were an additional constant added on one side?

**Tip:** Always double-check your work by substituting the solution back into the original equation.

Learn how to solve the equation 5(2a - 1) - 3a + 5 = 2(2a + 6) with a detailed step-by-step solution. This problem covers key algebraic concepts, including distributing constants, combining like terms, and isolating variables. Suitable for students in Grades 7-9.

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