Addition techniques are really helpful when we want to find the value of a variable in linear equations. By using smart addition or subtraction, we can break down equations step by step. This makes it easier to solve for the unknown variable.

Understanding the Basics

Let's look at a simple linear equation:

$$3x + 5 = 20$$

Here, our goal is to find out what $x$ is. To do this, we need to get rid of the number on the left side (the constant). We can use subtraction to make the equation simpler.

Step-by-Step Process

1. Subtract 5 from both sides: This means we take away 5 from each side:

   $$3x + 5 - 5 = 20 - 5$$

   This simplifies to

   $$3x = 15.$$

2. Divide both sides by 3: Now we need to get $x$ by itself. We do this by dividing:

   $$x = \frac{15}{3}$$

   which simplifies to

   $$x = 5.$$

From this example, we can see that addition or subtraction helps us clear out other numbers so we can focus on the variable.

Why Use Addition Techniques?

• Clarity: It helps make complex equations easier to understand.
• Flexibility: You can decide to add or subtract, depending on the equation.
• Simplification: Using smaller numbers makes calculations easier.

Another Example

Let’s try solving another equation:

$$x - 7 = 12.$$

To find $x$, we can use addition here too:

1. Add 7 to both sides:

   $$x - 7 + 7 = 12 + 7$$

   This simplifies to

   $$x = 19.$$

In summary, addition techniques help us isolate variables by letting us methodically get rid of other terms. Practicing these methods will make solving linear equations easier and more natural!