Question

Jaylin created the following expression: ON / (3 / 10 - 1 + 172 / 1 / 10). Jaylin created an equivalent expression using the following steps: 10 / (10x + (-12) + 12x + () + (-D). Is his final expression equivalent to the initial expression? Show how you know. If two expressions are not equivalent, find Jaylin's mistake and correct it.

Answer 1

The final expression is not equivalent to the initial expression. The mistake was not properly transferring the divisions and operations.

Step-by-step explanation:

Let's compare the two expressions:

Initial expression: ON / (3 / 10 - 1 + 172 / 1 / 10)

Equivalent expression: 10 / (10x + (-12) + 12x + () + (-D)

To determine if the two expressions are equivalent, we can simplify them:

For the initial expression:

1. Divide 3 by 10 = 0.3
2. Divide 172 by 0.1 = 1720
3. Subtract 1 from 0.3 = -0.7
4. Add the results: 0.3 + (-0.7) + 1720 = 1719.6
5. Divide ON by 1719.6 = ON / 1719.6

For the equivalent expression:

1. Combine like terms: 10x + 12x = 22x
2. Add up all the terms: 10 + (-12) + 22x + () + (-D) = -2 + 22x + () + (-D)
3. Divide 10 by -2 = -5
4. Divide -2 by -5 = 0.4
5. Divide -D by 0.4 = (-D) / 0.4

So, the initial expression is not equivalent to the equivalent expression. The mistake in Jaylin's expression is that they didn't properly transfer the divisions and operations.

The correct equivalent expression should be: -5 / (22x + () + (-D))