Combine the like terms to create an equivalent expression: 8t +1+(-4t) + (-6)
The correct answer and explanation is:
Combined Expression:
8t + 1 + (–4t) + (–6)
Step 1: Group the like terms
Like terms are terms with the same variable or constants. So we group:
- Variable terms: 8t and –4t
- Constant terms: +1 and –6
Step 2: Combine the like terms
- Combine variable terms:
8t – 4t = 4t - Combine constant terms:
1 – 6 = –5
Final Answer:
4t – 5
300-Word Explanation:
Combining like terms is a foundational skill in algebra. It allows you to simplify expressions and make equations easier to understand and solve. In the expression 8t + 1 + (–4t) + (–6), we’re dealing with both variable terms (those that include the variable t) and constant terms (numbers without variables).
The goal is to simplify the expression by combining terms that share the same characteristics. Variable terms like 8t and –4t are considered “like terms” because they both have the same variable, t, raised to the same power (in this case, the power is 1, which is usually not written). Constants like +1 and –6 are also like terms because they’re simply numbers.
To combine like terms:
- First, group the variable terms together: 8t and –4t. When you add them, you subtract 4t from 8t, which gives you 4t.
- Next, group the constants: +1 and –6. Adding these gives you –5.
Once you combine both parts, you get the simplified expression: 4t – 5. This expression is equivalent to the original but is much cleaner and easier to work with.
Why is this important? Simplifying expressions helps make solving equations faster and reduces the chance of making errors. It also helps in understanding relationships between quantities and making predictions based on mathematical models.
In summary, by identifying like terms and combining them using basic arithmetic, we transformed a cluttered expression into a streamlined one: 4t – 5. This is a key step in algebra that prepares you for more complex problem-solving.