The work of a student to solve a set of equations is shown:Equation 1: m = 8 + 2nEquation 2: 6m = 4 + 4nStep 1: −6(m) = −6(8 + 2n) [Equation 1 is multiplied by −6.]6m = 4 + 4n [Equation 2]Step 2: −6m = −48 − 12n [Equation 1 in Step 1 is simplified.]6m = 4 + 4n [Equation 2]Step 3: −6m + 6m = −48 − 12n + 4n [Equations in Step 2 are added.]Step 4: 0 = −48 − 8n Step 5: n = −6 In which step did the student first make an error? Step 3 Step 5 Step 4 Step 2
Accepted Solution
A:
The answer is: "Step 3" . _____________________________________________________ Note: "Step 3" incorrectly shows: "−6m + 6m = −48 − 12n + 4n " . ______________________________________________________ {Rather than the correct equation; which is:
" - 6m + 6m = - 48 – 12n + 4 + 4n " .}. ___________________________________________________ Note of interest: ___________________________________________________ Although not asked in the question/problem, let us continue with the correct equation; & to solve for" n ;
" - 6m + 6m = - 48 – 12n + (4 + 4n) ;
→ " 0 = - 48 – 12n + 4 + 4n " ; __________________________ Combine the "like terms" on the "right hand side of the equation: ___________________________ -48 + 4 = -44 ;
- 12n + 4n = - 8n ; __________________________
→ Rewrite the equation: " 0 = -8n – 44 " ;
↔ " - 8n – 44 = 0 " ;
Add "44" to each side of the equation;
→ -8n – 44 + 44 = 0 + 44 ;
to get:
→ -8n = 44 ;
Now, divide EACH SIDE of the equation by: "-8 " ; to isolate "n" on one side of the equation; & to solve for "n" ;