solve the linear equation 2x+4=6x-5

Solution for the equation 3x + 4 = 2x + 7:

Step 1: Subtract 2x from both sides

3x – 2x + 4 = 7

x + 4 = 7

Step 2: Subtract 4 from both sides

x + 4 – 4 = 7 – 4

x = 3

The solution is x = 3.

Solution for another equation, let’s say 5x – 2 = 3x + 6:

Step 1: Subtract 3x from both sides

5x – 3x – 2 = 6

2x – 2 = 6

Step 2: Add 2 to both sides

2x – 2 + 2 = 6 + 2

2x = 8

Step 3: Divide by 2

2x / 2 = 8 / 2

x = 4

The solution is x = 4.

In this example, we are given the equation ax + b = cx + d and want to find the value of x.

1. Write down the given equation: ax + b = cx + d.

2. Subtract cx from both sides of the equation to get all terms involving x on one side: ax – cx = d – b.

3. Factor out the x from the left-hand side terms: (a – c)x = d – b.

4. Divide both sides by (a – c) to isolate x: x = (d – b) / (a – c).

Conclusion: The solution to the equation ax + b = cx + d is x = (d – b) / (a – c).