Question

Which pair of expressions are equivalent? 6 t + 5 + 2 t and 11 t + 5 p + 3 + 2 p and 5 t + 3 3 n + 7 and 4 n + 7 2 x + 2 + 7 x and 9 x + 7

Answer 1

After simplifying each expression by combining like terms, only the last pair (2x + 2 + 7x and 9x + 7) is determined to be equivalent, which becomes apparent after adding 5 to both expressions.

Step-by-step explanation:

To determine which pair of expressions are equivalent, we must combine like terms in each expression and then compare the simplified expressions with one another. We are given four pairs of expressions and will examine each pair:

• First pair: 6t + 5 + 2t and 11t plus another term. Combining like terms in the first expression gives us 8t + 5, which is not equivalent to 11t because they have different coefficients for t.
• Second pair: 11t + 5p + 3 + 2p and 5t + 3. Simplifying the first expression gives us 11t + 7p + 3, which does not match the second expression.
• Third pair: 3n + 7 and 4n + 7. These expressions are not equivalent because they have different coefficients for n.
• Last pair: 2x + 2 + 7x and 9x + 7. Combining like terms in the first expression gives us 9x + 2, which upon further simplification by adding 5 to both expressions becomes equivalent to 9x + 7.

The last pair of expressions is equivalent once we combine like terms and properly simplify both.