- Distributing removes the parentheses in an expression.
- Following distribution, the standard algebraic procedure is to combine any like terms to simplify each side of the equation.
- By examining the procedural table, it is evident that "like terms" is the missing phrase.
- The final answer is \(\boxed{\text{like terms}}\).
Explanation
- Analyzing the Order of Operations
To determine the missing term, we analyze the logical sequence provided in the table for solving the linear equation \(3(x+5)-2=10\). The steps for solving a linear equation typically follow a structured order of operations:
- First, simplify the expression by distributing constants or coefficients to remove parentheses.
- Second, simplify each side of the equation further by grouping and combining identical types of terms, known as "like terms."
- Third, isolate the variable by performing inverse operations, starting with addition or subtraction.
- Fourth, finalize the isolation by performing inverse operations for multiplication or division.
Looking at the table provided, the step immediately following "Distribute (to get rid of parentheses)" is "Combine any Like Terms". The sentence to complete is "After using the distributive property, you use \(\_\_\_\_\) to combine on each side." Matching this to the sequence in the table, it is clear that the missing words are "like terms."
- Conclusion and Final Answer
Based on the table, the step that follows the distribution process is "Combine any Like Terms." By filling in the blank of the sentence, we confirm that "like terms" is the required term to complete the sequence of operations for solving the given linear equation. Therefore, after using the distributive property, you use like terms to combine on each side. The final answer is \(\boxed{\text{like terms}}\).
Examples
When organizing your desk, you might first distribute your items into piles: papers, pens, and books. After that, you "combine like terms" by putting all your pens in one container, all your papers in a folder, and all your books on a shelf. This process of organizing by category—or "like terms"—makes it much easier to manage your workspace, just as it makes solving a complex equation much more manageable. Whenever you face a large, scattered problem, remember to group your similar elements to simplify your path to the solution!