Math Problem Statement

solve: 1/2(x+3)=2(x-3)

Solution

We are given the equation:

12(x+3)=2(x3)\frac{1}{2}(x + 3) = 2(x - 3)

Step 1: Eliminate the fraction

Multiply both sides of the equation by 2 to eliminate the fraction:

(x+3)=4(x3)(x + 3) = 4(x - 3)

Step 2: Expand both sides

Expand both sides of the equation:

x+3=4x12x + 3 = 4x - 12

Step 3: Isolate the variable xx

Move all terms involving xx to one side and constant terms to the other side:

x4x=123x - 4x = -12 - 3

Simplify:

3x=15-3x = -15

Step 4: Solve for xx

Divide both sides by 3-3:

x=153=5x = \frac{-15}{-3} = 5

Thus, the solution is:

x=5x = 5

Would you like more details on any step, or do you have any questions?

Relative Questions:

  1. How can you check the solution of an equation?
  2. How do you handle equations with multiple variables?
  3. What is the difference between solving linear and quadratic equations?
  4. How can you solve equations involving fractions?
  5. What are the common mistakes when solving linear equations?

Tip:

Always check your solution by plugging it back into the original equation to verify it works!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Equation solving: ax + b = cx + d
Basic operations with fractions

Theorems

Property of equality
Distributive property

Suitable Grade Level

Grades 7-8