## Solving Equations with Variables on both Sides: Example

Let’s say that we have the following equation:

**4x – 5 + 3 = 2x + 1**

First we have to combine like terms. So, we will combine
constants with constants and variables with variables.

Step 1:

**4x – 5 + 3 = 2x + 1**

4x

**– 2x**= - 5 + 3**– 1****The reason I changed the signs when moving the variables and constants is because if I bring a positive to the other side it becomes negative and if I bring a negative to the other side it becomes a positive.**

Next we have to simplify.

Step 2:

**4x – 5 + 3 = 2x + 1**

**4x – 2x = - 5 + 3 - 1**

**2x = + 3 – 6**

**2x = - 3**

*Note: In order to simplify all I did was subtract the variables to get 2x and add*

*-5 + 3 -1 to get -3*

Step 3:

**4x – 5 + 3 = 2x + 1**

**4x – 2x = - 5 + 3 - 1**

**2x = + 3 – 6**

**2x = - 3**

Now we have a one-step equation. So, we’ll have to divide

**2x by 2 and -3 by 2**.**4x – 5 + 3 = 2x + 1**

**4x – 2x = - 5 + 3 - 1**

**2x = + 3 – 6**

**2x/2**

**= - 3/2**

**x**

**= - 3/2 or –1 1/2**

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