Math Problem Statement

Solve 2(6-3x)=6

Solution

Let's solve the equation 2(63x)=62(6 - 3x) = 6.

  1. First, distribute the 2 on the left-hand side: 2(63x)=2623x=126x2(6 - 3x) = 2 \cdot 6 - 2 \cdot 3x = 12 - 6x Now the equation becomes: 126x=612 - 6x = 6

  2. Subtract 12 from both sides to isolate the term with xx: 126x12=61212 - 6x - 12 = 6 - 12 6x=6-6x = -6

  3. Divide both sides by 6-6 to solve for xx: x=66=1x = \frac{-6}{-6} = 1

So, the solution is x=1x = 1.

Would you like more details or have any questions?


Here are 5 related questions to consider:

  1. What happens if you change the constant on the right-hand side, say 2(63x)=102(6 - 3x) = 10?
  2. How would you solve 3(42x)=93(4 - 2x) = 9?
  3. What are the steps to solve 52x=3x+75 - 2x = 3x + 7?
  4. Can you solve 4x3(2x)=74x - 3(2 - x) = 7?
  5. How do you solve 6(2x)=2(x+3)6(2 - x) = 2(x + 3)?

Tip: Always perform the distribution step carefully when solving equations involving parentheses.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Distributive Property

Formulas

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

Theorems

Basic Properties of Equality

Suitable Grade Level

Grades 6-8