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.
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.
