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Question

Solve 2(4n+1)+5(25n8)=62- 2 ( - 4 n + 1 ) + 5 \left( \frac { 2 } { 5 } n - 8 \right) = - 62

n=n =

Solution

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Step 1
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Using the Distributive Property,

2(4n+1)=(2)(4n)+(2)(1)=8n2-2 (-4n+1) = (-2)(-4n) + (-2)(1) = 8n-2

and

5(25n8)=5(25n)+5(8)=2n405 \qty(\dfrac{2}{5}n - 8) = 5 \qty(\dfrac{2}{5}n) + 5 (-8) = 2n - 40

Thus, the starting equation becomes

8n2+2n40=60(1)8n-2 + 2n-40 = -60 \tag{1}

Simplify the LHS:

8n2+2n40=(8n+2n)+(240)=10n428n-2+2n-40 = (8n+2n) + (-2-40) = 10n-42

Thus, (1) becomes

10n42=6210n-42 = -62

Add 42 to both sides and simplify:

10n42+42=62+4210n-42+42 = -62 + 42

10n=2010n = -20

Divide both sides by 10 and simplify

10n10=2010\dfrac{10n}{10} = \dfrac{-20}{10}

n=2\boxed{\color{#4257b2}n = -2}

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