Math Problem Statement

Expand and then simplify by collecting like terms for: c) 7 - 6(2x - 3) and e) 6 + 5(1 - 2x).

Solution

Let’s solve the given problems by expanding and simplifying as instructed.

Problem c: 76(2x3)7 - 6(2x - 3)

  1. Distribute the 6-6 to the terms inside the parentheses: 76(2x3)=712x+187 - 6(2x - 3) = 7 - 12x + 18

  2. Combine like terms (7+187 + 18): 2512x25 - 12x

Final Answer: 2512x25 - 12x


Problem e: 6+5(12x)6 + 5(1 - 2x)

  1. Distribute the 55 to the terms inside the parentheses: 6+5(12x)=6+510x6 + 5(1 - 2x) = 6 + 5 - 10x

  2. Combine like terms (6+56 + 5): 1110x11 - 10x

Final Answer: 1110x11 - 10x


Do you have any questions or want detailed explanations?
Here are 5 related questions to expand your learning:

  1. How do you handle negative signs during distribution?
  2. Why is combining like terms necessary in simplifying?
  3. How would the result change if there were additional variables?
  4. What happens if parentheses involve a fraction instead of an integer?
  5. Can you apply these steps to expand and simplify 2x+3(4x5)2x + 3(4x - 5)?

Tip: Always distribute multiplication before combining terms to avoid errors.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Simplifying Expressions
Distributive Property

Formulas

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

Theorems

Properties of equality for combining like terms

Suitable Grade Level

Grades 7-8