Math Problem Statement

6-4x=6x-8x+2

Solution

We need to solve the equation 64x=6x8x+26 - 4x = 6x - 8x + 2.

Step 1: Simplify both sides of the equation.

  • On the left-hand side, it stays the same: 64x6 - 4x.
  • On the right-hand side, combine like terms 6x8x6x - 8x to get 2x+2-2x + 2.

So the equation becomes: 64x=2x+26 - 4x = -2x + 2

Step 2: Move all terms involving xx to one side of the equation.

  • Add 4x4x to both sides to eliminate the 4x-4x from the left: 6=2x+26 = 2x + 2

Step 3: Isolate the variable xx.

  • Subtract 2 from both sides to get: 4=2x4 = 2x

  • Divide both sides by 2 to solve for xx: x=2x = 2

Final Answer:

x=2x = 2

Would you like any more details or have any questions?

Here are 5 related questions to expand your understanding:

  1. How would the solution change if the equation were 64x=6x+8x+26 - 4x = 6x + 8x + 2?
  2. Can you solve 64x=5x8x+46 - 4x = 5x - 8x + 4?
  3. What happens when both sides of the equation have the same coefficients for xx?
  4. How do you solve an equation with fractions, such as 64x2=6x8x+23\frac{6 - 4x}{2} = \frac{6x - 8x + 2}{3}?
  5. What are some examples of equations that don't have a solution?

Tip: Always simplify both sides of an equation first before trying to isolate the variable.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Combining Like Terms

Formulas

Linear equation of the form ax + b = cx + d

Theorems

Properties of Equality

Suitable Grade Level

Grades 7-8