Math Problem Statement

Rewrite in simplest terms: -7(-3t + 5) + 4t

Solution

Let's solve the given expression:

7(3t+5)+4t-7(-3t + 5) + 4t

Step 1: Distribute the 7-7 across the terms inside the parentheses.

7(3t+5)=(7)×(3t)+(7)×5=21t35-7(-3t + 5) = (-7) \times (-3t) + (-7) \times 5 = 21t - 35

So, the expression becomes: 21t35+4t21t - 35 + 4t

Step 2: Combine like terms (the terms involving tt).

21t+4t35=25t3521t + 4t - 35 = 25t - 35

Final Answer:

The expression simplified is: 25t3525t - 35

Would you like further clarification or a more detailed breakdown of any steps?


Here are 5 related questions for deeper understanding:

  1. How can you simplify an expression involving multiple parentheses and terms?
  2. What is the distributive property and why is it important?
  3. How do you combine like terms when simplifying algebraic expressions?
  4. What is the difference between terms and coefficients in an algebraic expression?
  5. How would you solve an equation that contains the expression 25t3525t - 35?

Tip: Always perform operations like distribution and combining like terms carefully, step by step, to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Algebra
Distributive Property
Combining Like Terms

Formulas

Distributive property: a(b + c) = ab + ac

Theorems

Distributive Property

Suitable Grade Level

Grades 7-9