Question

A student is asked to solve the equation 3k – 16 = 55 for k. their work is shown. original problem 3k – 16 = 55 step one –16 –16 step two 3k = 39 step three 3k divided by 3 equals 39 divided by 3 step four k = 13 the student made a mistake in step one. what operation should the student have performed?

Answer 1

The mistake the student made was subtracting 16 instead of adding 16 in the first step to solve for k. After correctly adding 16, dividing by 3 gives the solution k = 23.67.

Step-by-step explanation:

The student is asked to solve the equation 3k – 16 = 55 for k. To isolate k, the student must perform the inverse operation to undo the subtraction of 16 from 3k. In step one, the correct operation is to add 16 to both sides of the equation, not subtract 16. Here's how the correct steps should look:

1. 
   
3. Add 16 to both sides: 3k - 16 + 16 = 55 + 16
4. 
   
6. Simplify: 3k = 71
7. 
   
9. Divide both sides by 3: 3k / 3 = 71 / 3
10. 
    
12. Solve for k: k = 23.67

The student's error in step one was subtracting 16 instead of adding 16. The correct answer after following the proper operations is k = 23.67.