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

Answer:

The error was that Jordan didn't take into account the minus sign in the step 3. The solution of the equation is $x=-\frac{23}{7}$

Step-by-step 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. $\frac{-7x}{7}=\frac{23}{7}$,          the step 3 is correct.
4. $x=\frac{23}{7}$,           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. $\frac{-7x}{7}=\frac{23}{7}$
4. $-x=\frac{23}{7}$
5. $-x\cdot (-1)=\frac{23}{7}\cdot (-1)$
6. $x=-\frac{23}{7}$

Thus, the error was that Jordan didn't take into account the minus sign in the step 3. The solution of the equation is $x=-\frac{23}{7}$