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.
To simplify the expression 5.4t+6.7+1.8t−4.35.4t + 6.7 + 1.8t – 4.3, follow these steps:
- Group the like terms: In the expression, 5.4t5.4t and 1.8t1.8t are both terms with the variable tt, and 6.76.7 and −4.3-4.3 are constants (terms without the variable tt).
- Combine the like terms:
- For the tt-terms: 5.4t+1.8t=(5.4+1.8)t=7.2t5.4t + 1.8t = (5.4 + 1.8)t = 7.2t
- For the constants: 6.7−4.3=2.46.7 – 4.3 = 2.4
- Write the simplified expression: After combining like terms, the expression becomes: 7.2t+2.47.2t + 2.4
Thus, the expression 5.4t+6.7+1.8t−4.35.4t + 6.7 + 1.8t – 4.3 simplifies to 7.2t + 2.4.
This approach is based on the distributive property, which allows combining terms with the same variable. By grouping terms with tt together and constants separately, you can simplify the expression to a form that is easier to work with, especially in solving equations or further algebraic manipulations.