How can you use properties to solve equations with a variable on both side so of the equal sign?

Solving equations with a variable on both sides requires multiple steps. Let's look at how to solve one using properties step by step.

Example 1: 100 - 4x = 16x

Step 1: In the above equation, the first step is to identify the variable. Clearly, it is x but the variable exists on both sides of the equal sign.

Step 2: To simplify it, we can use the properties of equality (addition and multiplication property of equality) which says that if we perform an operation on one side, the same should be done on the other side of the equal sign so that the equation is balanced.

Using the addition property of equality, let's add 4x to both sides, we get.

100 - 4x + 4x = 16x +4 x

which equals, 100 = 20x

Now, dividing both sides by 20, we get

x = 5

For more complex equations, the usage of distributive property of multiplication might be needed to isolate the variable and simplify.