Solve forn: -6(n-8) = 4(12-5n)+14n

Mathematics

2 answers:

Dominik [7]4 years ago

6 0

$\huge\text{Hey there!}$

$\huge\text{-6(n - 8) = 4(12 - 5n)}$

$\huge\text{First, \bf{distribute}}\text{ the terms}$

Formula is: a ( b + c) = a(b) + a(c) = ab + ac

$\huge\text{First set}\downarrow$

$\text{-6(n - 8)}\\\text{-6(n) - 6(-8)}\\\text{-6(n) = -6n}\\\text{-6(-8) = 48}\\\boxed{\text{Result for the left side:-6n +48}}$

$\huge\text{Second set}\downarrow$

$\text{4(12-n)}\\\text{4(12 - 5n)}\\\text{4(12)-4(-5n)}\\\text{4(12) = 48}\\\text{4(-5n) = -20n}\\\boxed{\text{Result for the right side 48 + (-20)}}$

$\text{We get:-6n +48 +20n=-20n+ 48+ 20n}$

→ = 14n+48 = 48

$\huge\text{Now, you have to SUBTRACT by 48 on your}\\\huge\text{sides.}$

$\text{14n + 48 \bf{ - 48}}\text{ = 48 - \bf{48}}$

$\text{Cancel out the second: 48 - 48 because it equals 0}$

$\text{Keep the first one because it helps us solve for our answer}$

$\text{14n = 0}\\\text{Divide both sides by the number \bf{14}}$

$\dfrac{\text{14n}}{14} = \dfrac{0}{14}\\\\\text{Cancel out}\dfrac{\text{14n}}{14}\text{ because it equals to one and we don't need it for this problem}\\\\\\\text{Keep: }\dfrac{0}{14}\text{ because it helps us solve for our answer.}$