Simplify: $2t + 1 - t + 4 + 3t - 2 = 4t + 3 = 15$. - Coaching Toolbox
Simplify: How to Solve the Equation $2t + 1 - t + 4 + 3t - 2 = 4t + 3 = 15$ Step-by-Step
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:
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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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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:
$$
t = rac{12}{4} = 3
$$
