Math Problem Statement

Simplify each expression: 10. 8(3x + 4) - 20, 12. 4(2x + 3) + 6x + 9, 14. (1/3)(6x - 15) - 3x

Solution

Let's simplify the expressions from the image you uploaded.

Problem 10:

Expression: 8(3x+4)208(3x + 4) - 20

Steps:

  1. Distribute the 8 to each term inside the parentheses: 8(3x)+8(4)=24x+328(3x) + 8(4) = 24x + 32
  2. Subtract 20: 24x+3220=24x+1224x + 32 - 20 = 24x + 12

Simplified form: 24x+1224x + 12


Problem 12:

Expression: 4(2x+3)+6x+94(2x + 3) + 6x + 9

Steps:

  1. Distribute the 4: 4(2x)+4(3)=8x+124(2x) + 4(3) = 8x + 12
  2. Add 6x+96x + 9: 8x+12+6x+9=14x+218x + 12 + 6x + 9 = 14x + 21

Simplified form: 14x+2114x + 21


Problem 14:

Expression: 13(6x15)3x\frac{1}{3}(6x - 15) - 3x

Steps:

  1. Distribute 13\frac{1}{3}: 13(6x)+13(15)=2x5\frac{1}{3}(6x) + \frac{1}{3}(-15) = 2x - 5
  2. Subtract 3x3x: 2x53x=x52x - 5 - 3x = -x - 5

Simplified form: x5-x - 5


Would you like me to proceed with more simplifications, or do you have any specific questions?

Here are 5 related questions for further exploration:

  1. How do you simplify expressions with multiple sets of parentheses?
  2. What is the difference between distributing and factoring in algebra?
  3. How do you handle negative coefficients when simplifying?
  4. Can you solve expressions with variables on both sides of the equation?
  5. How do operations with fractions differ from whole numbers in algebra?

Tip: Always perform operations inside parentheses first, then distribute and combine like terms.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplifying Expressions
Distributive Property

Formulas

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

Theorems

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Suitable Grade Level

Grades 7-9