Question

Jordan solved the equation −7x + 25 = 48; his work is shown below. Identify the error and where it was made. (5 points)

−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

a
Step 1: He should have added 25 to each side.

b
Step 1: He should have divided both sides by −7.

c
Step 3: He should have divided both sides by −7.

d
Step 3: He should have multiplied both sides by −7.

Answer 1

Jordan's error occurred in step 2 of the equation when performing the subtraction. The correct result of the expression 48 - 25 is 23, not 23. After correcting the arithmetic mistake, the correct solution is x = -23/7.

Step-by-step explanation:

Jordan made an error in step 2 of solving the equation −7x + 25 = 48. The mistake is in the arithmetic operation performed on the constants:

Step 1: −7x + 25 − 25 = 48 − 25
This step involves subtracting 25 from both sides of the equation, which is correct. However, when calculating the result on the right side of the equation, an error was committed.

Step 2: −7x = 23
After subtracting 25 from 48, the correct result should be 23. The correct subtraction is:

48 - 25 = 23

Step 3: −7x / −7 = 23 / −7
This step is correct, where you divide both sides by -7 to solve for x.

Step 4: x = 23 / −7
This is the correct final answer, meaning that Jordan's error occurred with the arithmetic in step 2.

To rectify the error, Jordan should have computed 48 - 25 correctly. The correct calculation is:

48 - 25 = 23, not 23 as initially stated by Jordan.

Once the correct subtraction is done, the remaining steps are carried out accurately to find the solution to the equation, which will be x = -23 / 7.