Simplify: How to Solve the Equation $2t + 1 - t + 4 + 3t - 2 = 4t + 3 = 15$ Step-by-Step

Solving equations is a fundamental skill in algebra, and simplifying complex expressions often makes the process clearer and easier. One common equation students encounter is:

$$
2t + 1 - t + 4 + 3t - 2 = 4t + 3 = 15
$$

Understanding the Context

At first glance, this looks daunting, but with careful step-by-step simplification, you can solve for $ t $ efficiently. This article breaks down how to simplify the left-hand side, combine like terms, isolate the variable, and solve the equation.

Step 1: Combine Like Terms on the Left Side

The left side of the equation is:

Simplify: $2t + 1 - t + 4 + 3t - 2 = 4t + 3 = 15$.

Key Insights

$$
2t + 1 - t + 4 + 3t - 2
$$

Group all the terms involving $ t $ and constant terms:

  • Combine $ t $-terms: $ 2t - t + 3t = (2 - 1 + 3)t = 4t $
  • Combine constant terms: $ 1 + 4 - 2 = 3 $

So, the left-hand side simplifies to:

$$
4t + 3
$$

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Final Thoughts

Thus, the equation becomes:

$$
4t + 3 = 15
$$

Step 2: Isolate the Variable Term

Now, subtract 3 from both sides to eliminate the constant:

$$
4t + 3 - 3 = 15 - 3
$$
$$
4t = 12
$$

Step 3: Solve for $ t $

Divide both sides by 4:

$$
t = rac{12}{4} = 3
$$