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Question

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

Solution

Verified
Step 1
1 of 2

Using the Distributive Property,

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

and

$5 \qty(\dfrac{2}{5}n - 8) = 5 \qty(\dfrac{2}{5}n) + 5 (-8) = 2n - 40$

Thus, the starting equation becomes

$8n-2 + 2n-40 = -60 \tag{1}$

Simplify the LHS:

$8n-2+2n-40 = (8n+2n) + (-2-40) = 10n-42$

Thus, (1) becomes

$10n-42 = -62$

Add 42 to both sides and simplify:

$10n-42+42 = -62 + 42$

$10n = -20$

Divide both sides by 10 and simplify

$\dfrac{10n}{10} = \dfrac{-20}{10}$

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

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