Solve the equation.
3(t + 7) + 2 = 6t - 2 + 2t
The answer is 5. Am I correct?
Right. t = 5
Proof:
3(t + 7) + 2 = 6t - 2 + 2t
3(12) + 2 = 30 - 2 + 10
38 = 28 + 10
To solve this equation, we will start by simplifying both sides of the equation and combining like terms. Then, we will isolate the variable t.
Let's follow these steps:
1. Distribute the 3 on the left side: 3(t + 7) = 3t + 21.
2. Combine like terms on the left side: 3t + 21 + 2 = 3t + 23.
3. Simplify the right side: 6t - 2 + 2t = 8t - 2.
4. Now, our equation becomes: 3t + 23 = 8t - 2.
5. Next, we want to isolate the variable t by getting all the t terms on one side of the equation. To do this, we can subtract 3t from both sides: 3t - 3t + 23 = 8t - 3t - 2.
This simplifies to: 23 = 5t - 2.
6. We move the constant term -2 to the other side of the equation by adding 2 to both sides: 23 + 2 = 5t.
This simplifies to: 25 = 5t.
7. Finally, to solve for t, divide both sides of the equation by 5: 25/5 = t.
This simplifies to: 5 = t.
So, the solution to the equation is t = 5.