Q:

# 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" .
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Note:  "Step 3"  incorrectly shows:   "−6m + 6m =  −48 − 12n + 4n " .
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{Rather than the correct equation; which is:

" - 6m + 6m =  - 48 – 12n + 4 + 4n " .}.
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Note of interest:
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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 " ;
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Combine the "like terms" on the "right hand side of the equation:
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-48 + 4 = -44 ;

- 12n + 4n = - 8n ;
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→ 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" ;

→    -8n / 8 = 44 / 8 ;

→     n = 44/8 = (44 ÷ 4) / (8÷4) = 11/2 ;

n =  "$$\frac{11}{2}$$"  ; or, write as:  "5 $$\frac{1}{2}$$"  ;

or, write as:  " 5.5 " .
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