Question

Jordan solved the equation −7x + 25 = 48; his work is shown below. Identify the error and where it was made. −7x + 25 = 48 Step 1: −7x + 25 − 25 = 48 − 25 Step 2: −7x = 23 Step 3: negative seven times x over seven = twenty-three over seven Step 4: x = twenty-three over seven

Answer 1

the problem seems to be correct there should be there aren't any mistakes right?

Answer 2

The error was that Jordan didn't take into account the minus sign in the step 3. The solution of the equation is
`x=-(23)/(7)`

Explanation:

The steps to solve the equation
`-7x+25=48` would be:

1. 
   `-7x+25-25=48-25`, the step 1 is correct.
2. 
   `-7x=23`, the step 2 is correct
3. 
   `(-7x)/(7)=(23)/(7)`, the step 3 is correct.
4. 
   `x=(23)/(7)`, the step 4 is INCORRECT

The step 4 is incorrect because the minus sign in the step 3 was not taken into account. The correct steps would be:

1. 
   `-7x+25-25=48-25`
2. 
   `-7x=23`
3. 
   `(-7x)/(7)=(23)/(7)`
4. 
   `-x=(23)/(7)`
5. 
   `-x\cdot (-1)=(23)/(7)\cdot (-1)`
6. 
   `x=-(23)/(7)`

Thus, the error was that Jordan didn't take into account the minus sign in the step 3. The solution of the equation is
`x=-(23)/(7)`