You are solving an equation and have simplified each side. You see that there is a term containing the variable on each side, both having a negative coefficient. Explain what you would choose to do and why.

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Sometimes, the unknown quantity will appear on both sides of an equation. This is where the properties learned in 5.1 and 5.2 come in handy. A quantity with a variable can be treated just like a quantity without variables -- a quantity with a variable follows all the rules learned in the last two sections. For example, we can add a quantity with a variable to both sides without changing the equation or the values that make it true:

15 - x = 4x

15 - x + x = 4x + x

15 + 0x = 5x

15 = 5x

3 = x

x = 3

Step-by-step explanation:

In other words, we must add to both sides or subtract from both sides one of the quantities that contains the variable. It is generally easier to add or to subtract the smaller quantity from the larger quantity, so we are working with positive coefficients, but either way works. Once the variable is on one side only, we can proceed using inverse operations, as in 4.1 and 4.2.