Find The Value Of X If The Arithmetic Mean Of 3 And 3x + 5 Is 8

Find the value of x if the arithmetic mean of 3 and 3x + 5 is 8

 

Answer:

x = 8/3

Step-by-step explanation:

Arithmetic Mean = (a₁ + an)/2

Given:

Mean: 8

a₁: 3

an: 3x+5

Equation:

8 = (3 + 3x+5)/2

8(2) = 3 + 3x+5

16 = 3x + 8

3x = 16-8

3x/3 = 8/3

x = 8/3

Check:

a₁: 3

an: 3(8/3) + 5 = 13

Mean: 8

(3+13)/2 = 8

16/2 = 8

8 = 8  (True)