Question

Anna and Belle are asked to solve −2x − 15 = 6x + 9. Identify where one of them made an error. Anna Belle −2x − 15 = 6x + 9 −2x − 15 −6x = 6x + 9 −6x −8x − 15 = 9 −8x − 15 + 15 = 9 + 15 −8x = 24 Negative 8x over negative 8 equals 24 over negative 8 x = −3 −2x − 15 = 6x + 9 −2x − 15 + 2x = 6x + 9 + 2x −15 = 8x + 9 −15 + 9 = 8x + 9 + 9 −6 = 8x Negative 6x over 8 equals 8x over 8 Negative two-thirds

Answer 1

Belle got it wrong when she added the 9 because it was already positive, meaning she would’ve subtracted it.

Answer 2

Belle is wrong.

Explanation:

The given expression is

`-2x-15=6x+9`

The steps Anna did are

`-2x-15=6x+9\\-2x-15-6x=6x+9-6x\\-8x-15=9\\-8x-15+15=9+15\\-8x=24\\(-8x)/(-8)=(24)/(-8) \\x=-3`

If you look carefuly, you would notice that Anna didn't make any mistakes, her steps and result is correct.

Belle steps are

`-2x-15=6x+9\\-2x-15+2x=6x+9+2x\\-15=8x+9\\-15+9=8x+9+9`

Notice that this step is wrong, because she's not adding -9 to eliminate that term.

`-6=8x`, this step is also wrong, because 9 + 9 = 18.

Therefore, Belle is wrong.