How do i solve 2/3(x+7) = 10?

Question

2(x+7)/3 = 10
(2x +14)/3 = 10
(3)(2x +14/)3 = 10*3
2x + 14 = 30
2x = 30-14
2x = 16
x = 8

why wouldnt' I distribute 2/3 to x + 7 and get 2/3x + 14/3?

choices were a. 22, b. 8, c. -1/3, d. 41/3.
I started out doing this (but couldn't get any of those answers)
2/3x + 14/3 = 10
2/3x = 10 - 14/3
2/3x = 9 3/3 - 14/3 14/3 = 4 2/3
2/3x = 5 2/3
(3/2)2/3x = 5 2/3 (3/2)
x = 5 1/2

Answer 1

Your error is after
2/3x = 10 - 14/3

(2/3)x = 30/3 - 14/4 = 16/3 , you had 14/3
multiply each side by 3
2x = 16
x = 8

Don't work with mixed fractions, it becomes very messy that way.
Mixed fractions look very pretty as final answers, but are useless in calculations.

Answer 2

clearly, x=8 is the solution, since
2/3(8+7) = 10 = 2/3 (15) = 10

Answer 3

btw, I noticed other errors after your 4th last line
you had:
2/3x = 9 3/3 - 14/3 14/3 = 4 2/3
2/3x = 5 2/3 , how did 4 2/3 become 5 2/3
(3/2)2/3x = 5 2/3 (3/2)
x = 5 1/2

5 2/3 (3/2) = (17/3)(3/2)
= 17/2 or 8 1/2 <------ which of course was not the answer, but what you should have obtained

see what I mean about mixed fractions?

Answer 4

Oobleck you confuse the student by giving direct but often incomprehensible answers to students.

The step-by-step solution is more understandable.

( 2 / 3 ) ( x + 7 ) = 10

Multiply both sides by 3

2 ( x + 7 ) = 30

2 ∙ x + 2 ∙ 7 = 30

2 x + 14 = 30

Subtract 14 to both sides

2 x + 14 - 14 = 30 - 14

2 x = 16

Divide both sides by 2

x = 8

Answer 5

the solution had already been given.
what is so hard about checking the result? 2/3 (15) is somehow confusing?

Answer 6

Thanks all!