Which expression is equivalent to 5.4t + 6.7 + 1.8t – 4.3 ?
9.6t
9.6
3.6t + 11
7.2t + 2.4
The correct answer and explanation is:
The correct answer is 7.2t + 2.4.
Explanation:
To simplify the expression 5.4t+6.7+1.8t−4.35.4t + 6.7 + 1.8t – 4.3, follow these steps:
- Group like terms:
- The terms involving tt are 5.4t5.4t and 1.8t1.8t.
- The constant terms are 6.76.7 and −4.3-4.3.
- Simplify the terms involving tt:
- Add 5.4t5.4t and 1.8t1.8t together: 5.4t+1.8t=7.2t5.4t + 1.8t = 7.2t
- Simplify the constant terms:
- Add 6.76.7 and −4.3-4.3 together: 6.7−4.3=2.46.7 – 4.3 = 2.4
- Combine the results:
- Now, combine the simplified terms: 7.2t+2.47.2t + 2.4
Thus, the expression simplifies to 7.2t + 2.4, which matches the fourth option.
In algebra, simplifying expressions like this is a key step in solving equations or performing operations on polynomials. Combining like terms helps to make the expression more manageable and easier to work with in later steps, whether you’re solving for a variable or performing further operations.