Final answer:
To combine like terms in an equation, we use addition or subtraction, and for balancing weight on a scale in multi-step problems, we may also employ multiplication or division, along with conversion of units between grams and kilograms.
Step-by-step explanation:
To combine like terms, we utilize addition or subtraction to consolidate terms with the same variable raised to the same power. In the context of a balance scale, if you have a term like +2 on one side and you wish to move it to the other side, you would use the operation of subtraction. For instance, if your equation is x + 2 = 5, to solve for x, you need to subtract 2 from both sides to keep the scale balanced, resulting in x = 3. Similarly, when dealing with weight in grams or kilograms, you may use addition or subtraction to balance an equation involving several weights.
When faced with multi-step problems that require finding the weight of objects and balancing the scale, multiplication or division may also come into play. For example, if you know the total weight on one side and the number of items contributing to that weight, division will help you find the weight of a single item. Conversely, if you know the weight of a single item and need to find the total weight of multiple items, you will use multiplication.
When considering problems of this nature, you may also need to convert compound units, such as converting grams to kilograms or vice versa, to accurately compare and balance weights. This conversion ensures that all weights are expressed in the same units before any addition or subtraction is done.