Math Problem Statement

Solve for x: 3x − 5 = 2x + 6.

Solution

To solve the equation 3x5=2x+63x - 5 = 2x + 6, follow these steps:

  1. Subtract 2x2x from both sides: 3x2x5=63x - 2x - 5 = 6 Simplifying this gives: x5=6x - 5 = 6

  2. Add 5 to both sides: x5+5=6+5x - 5 + 5 = 6 + 5 Simplifying this gives: x=11x = 11

So, the solution is x=11x = 11.

Would you like further clarification, or do you have any other questions? Here are five related questions:

  1. How would you solve 4x7=3x+94x - 7 = 3x + 9?
  2. What happens if you add a constant to both sides of an equation?
  3. How would the equation change if it were 3x5=2x63x - 5 = 2x - 6?
  4. Can you solve 5x3=7x+45x - 3 = 7x + 4 and compare the process?
  5. How can you check if your solution for xx is correct?

Tip: When solving equations, always try to isolate the variable by performing the same operations on both sides.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Basic linear equation: ax + b = cx + d

Theorems

Equality property of equations

Suitable Grade Level

Grades 6-8