Question

Jaylin created the following expression: 25x − 310 − x + 1710x − 110. Jaylin created an equivalent expression using the following steps: 410x + (−1x) + 1710x + (−310) + (−110). Is his final expression equivalent to the initial expression? Show how you know. If the two expressions are not equivalent, find Jaylin's mistake and correct it.

a) Yes, the expressions are equivalent.
b) No, the expressions are not equivalent.

Answer 1

No, the expressions are not equivalent because Jaylin did not combine the like terms in his final expression. The correct equivalent expression is 1734x - 420.

Step-by-step explanation:

No, the expressions are not equivalent. To determine if two expressions are equivalent, we need to simplify them and compare the results. In the initial expression, all the terms are combined together. However, in Jaylin's final expression, the terms are separated by addition. To correct this, Jaylin should combine like terms in his final expression. Here are the steps to simplify the expressions:

Initial expression: 25x - 310 - x + 1710x - 110

Combine like terms: (25x - x + 1710x) + (-310 - 110)

Simplify: 1734x - 420

Jaylin's mistake was not combining the like terms in his final expression. The correct equivalent expression is 1734x - 420. Therefore, the answer is b) No, the expressions are not equivalent.