Question

Erica solved the equation −5x − 25 = 78; her work is shown below. Identify the error and where it was made. −5x − 25 = 78 Step 1: −5x − 25 − 25 = 78 − 25 Step 2: −5x = 53 Step 3: negative five times x over negative five = fifty-three over negative five Step 4: x = negative fifty-three over five Step 1: She should have added 25 to each side. Step 1: She should have divided both sides by −5. Step 3: She should have divided both sides by −5. Step 3: She should have multiplied both sides by −5.

Answer 1

Have you tried solving x yourself to possibly identify the error? 

We know that if we have something like 
2x - 3 = 2 and to solve for x, we have to get x alone as much as we can.  We have to take the opposite of -3 (which is +3) and add it to both sides of the equations
2x - 3 + 3 = 2 +3 , what that does is cancel out the three on both sides.

For this situation Erica has -5x -25 = 78 the first step she took to try and get x alone as much as she could was to subtract 25 on both sides, which is wrong!!
-5x - 25 - 25 = 78 -25 does not cancel 25 on the left hand side. In fact it doubles it.

So Erica messed up on step 1. She should have added 25 on both sides. 

Answer 2

Hi there! Her mistake is in step 1.

She subtracted -25 by 25. -25 - 25 = -50

What she SHOULD have done was add 25 to each side. This obeys the property of reciprocals.

-25 + 25 = 0

Hope this helps.

:)