5n – 3 = |n +9|
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Step-by-step explanation:

Simplifying

5n + -3 = 9 + -1n

Reorder the terms:

-3 + 5n = 9 + -1n

Solving

-3 + 5n = 9 + -1n

Solving for variable 'n'.

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

Add 'n' to each side of the equation.

-3 + 5n + n = 9 + -1n + n

Combine like terms: 5n + n = 6n

-3 + 6n = 9 + -1n + n

Combine like terms: -1n + n = 0

-3 + 6n = 9 + 0

-3 + 6n = 9

Add '3' to each side of the equation.

-3 + 3 + 6n = 9 + 3

Combine like terms: -3 + 3 = 0

0 + 6n = 9 + 3

6n = 9 + 3

Combine like terms: 9 + 3 = 12

6n = 12

Divide each side by '6'.

n = 2

Simplifying

n = 2

n-3

Step-by-step explanation:

Simplifying

5n + 3 = n + -9

Reorder the terms:

3 + 5n = n + -9

Reorder the terms:

3 + 5n = -9 + n

Solving

3 + 5n = -9 + n

Solving for variable 'n'.

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

Add '-1n' to each side of the equation.

3 + 5n + -1n = -9 + n + -1n

Combine like terms: 5n + -1n = 4n

3 + 4n = -9 + n + -1n

Combine like terms: n + -1n = 0

3 + 4n = -9 + 0

3 + 4n = -9

Add '-3' to each side of the equation.

3 + -3 + 4n = -9 + -3

Combine like terms: 3 + -3 = 0

0 + 4n = -9 + -3

4n = -9 + -3

Combine like terms: -9 + -3 = -12

4n = -12

Divide each side by '4'.

n = -3

Simplifying

n = -3

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: