Solve Linear Equation: 19 = 3a - 6 + 4a - 2a Step by Step

To solve this problem, we'll follow these steps:

• Step 1: Simplify the equation by combining like terms.
• Step 2: Isolate the variable $a$ to find its value.
• Step 3: Verify the solution by substitution.

Now, let's work through each step:
Step 1: The given equation is $19 = 3a - 6 + 4a - 2a$.
First, combine the like terms involving $a$:
$3a + 4a - 2a = 5a$.
Now, the equation simplifies to $19 = 5a - 6$.

Step 2: Isolate $a$ by first adding 6 to both sides of the equation to eliminate the constant term on the right side:
$19 + 6 = 5a$
$25 = 5a$.

Next, divide both sides by 5 to solve for $a$:
$a = \frac{25}{5}$
$a = 5$.

Step 3: Verify the solution:
Substitute $a = 5$ back into the original equation:
$19 = 3(5) - 6 + 4(5) - 2(5)$
Calculate each term: $3(5) = 15$, $4(5) = 20$, and $2(5) = 10$.
Therefore, $19 = 15 - 6 + 20 - 10$, which simplifies to $19 = 19$, confirming our solution is correct.

Therefore, the solution to the problem is $a = 5$.