Question

Which of the following shows whether the expressions 5(t-1)+8 and 2t+3(t+1) are equivalent?

Answer 1

To verify if 5(t-1)+8 and 2t+3(t+1) are equivalent, both expressions are simplified to show they result in the same expression, which is 5t + 3, confirming their equivalence.

Step-by-step explanation:

To determine whether the expressions 5(t-1)+8 and 2t+3(t+1) are equivalent, we need to simplify both expressions and see if they result in the same expression.

First, let's simplify the expression 5(t-1)+8:

1. Distribute the 5 into the parentheses: 5 × t - 5 × 1 + 8 = 5t - 5 + 8.
2. Combine like terms: 5t + (8 - 5) = 5t + 3.

Now, let's simplify the expression 2t+3(t+1):

1. Distribute the 3 into the parentheses: 2t + (3 × t + 3 × 1) = 2t + 3t + 3.
2. Combine like terms: (2t + 3t) + 3 = 5t + 3.

Both expressions simplify to 5t + 3. Therefore, the expressions are equivalent.