Question

Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. She knows she made a mistake, but she can’t find it. Where is Clare's mistake?

Answer 1

In the second step 12 times 5 does not equal 72 so that is the mistake

Answer 2

The Second Step.

Explanation:

We are given the original equation:

`12(5+2y)=4y-(5-9y)`

In her first step, Clare distributed both sides:

`72+24y=4y-5-9y`

There are two errors:

First, the product of 5 and 12 is 60 and not 72.

Second, on the right-hand side of the equation, the negative must be distributed to all terms. Hence, the correct result should be:

`\displaystyle 60 + 24y = 4y - 5 + 9y`

Instead of what she had obtained.