Question

3 (n-4)+2 (4n-5) = 5(n+2)+16
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Answer 1

Step-by-step explanation:

Simplifying

3(n + -4) + 2(4n + -5) = 5(n + 2) + 16

Reorder the terms:

3(-4 + n) + 2(4n + -5) = 5(n + 2) + 16

(-4 * 3 + n * 3) + 2(4n + -5) = 5(n + 2) + 16

(-12 + 3n) + 2(4n + -5) = 5(n + 2) + 16

Reorder the terms:

-12 + 3n + 2(-5 + 4n) = 5(n + 2) + 16

-12 + 3n + (-5 * 2 + 4n * 2) = 5(n + 2) + 16

-12 + 3n + (-10 + 8n) = 5(n + 2) + 16

Reorder the terms:

-12 + -10 + 3n + 8n = 5(n + 2) + 16

Combine like terms: -12 + -10 = -22

-22 + 3n + 8n = 5(n + 2) + 16

Combine like terms: 3n + 8n = 11n

-22 + 11n = 5(n + 2) + 16

Reorder the terms:

-22 + 11n = 5(2 + n) + 16

-22 + 11n = (2 * 5 + n * 5) + 16

-22 + 11n = (10 + 5n) + 16

Reorder the terms:

-22 + 11n = 10 + 16 + 5n

Combine like terms: 10 + 16 = 26

-22 + 11n = 26 + 5n

Solving

-22 + 11n = 26 + 5n

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-5n' to each side of the equation.

-22 + 11n + -5n = 26 + 5n + -5n

Combine like terms: 11n + -5n = 6n

-22 + 6n = 26 + 5n + -5n

Combine like terms: 5n + -5n = 0

-22 + 6n = 26 + 0

-22 + 6n = 26

Add '22' to each side of the equation.

-22 + 22 + 6n = 26 + 22

Combine like terms: -22 + 22 = 0

0 + 6n = 26 + 22

6n = 26 + 22

Combine like terms: 26 + 22 = 48

6n = 48

Divide each side by '6'.

n = 8

Simplifying

n = 8