Math Problem Statement

Solve the equation 4x + 1 = 2x - 5

Solution

The equation visible in the image is:

4x+1=2x54x + 1 = 2x - 5

Let’s solve this step-by-step:

Step 1: Move all terms involving xx to one side.

Subtract 2x2x from both sides: 4x2x+1=54x - 2x + 1 = -5 2x+1=52x + 1 = -5

Step 2: Move the constant to the other side.

Subtract 1 from both sides: 2x=512x = -5 - 1 2x=62x = -6

Step 3: Solve for xx.

Divide both sides by 2: x=62x = \frac{-6}{2} x=3x = -3

The solution to the equation is x=3x = -3.

Would you like further details or have any questions?

Here are some related questions for practice:

  1. How would you check if x=3x = -3 is a correct solution?
  2. What happens if you move the constants first instead of the variables?
  3. Solve the equation 5x7=3x+95x - 7 = 3x + 9.
  4. How would you solve the equation 7x+2=4x107x + 2 = 4x - 10?
  5. How can equations like this be applied in real-world problems?

Tip: Always simplify equations step-by-step and move terms logically to avoid mistakes.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Algebra

Formulas

Basic linear equation: ax + b = cx + d

Theorems

Addition and Subtraction Properties of Equality

Suitable Grade Level

Grades 6-8