How do i solve 2/3(x+7) = 10?
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
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.
clearly, x=8 is the solution, since
2/3(8+7) = 10 = 2/3 (15) = 10
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?
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
the solution had already been given.
what is so hard about checking the result? 2/3 (15) is somehow confusing?
Thanks all!
To solve 2/3(x+7) = 10, you want to isolate the variable x. Here's the correct step-by-step solution:
1. Distribute the 2/3 to both terms inside the parentheses:
(2/3) * (x+7) = 10
2. Multiply 2/3 by x and 2/3 by 7:
(2/3)x + (2/3)*7 = 10
3. Simplify:
(2/3)x + (14/3) = 10
4. Next, to remove the fraction from (2/3)x, you need to multiply the entire equation by the reciprocal of 2/3, which is 3/2:
(3/2) * [(2/3)x + (14/3)] = (3/2) * 10
5. Simplify:
(3/2) * (2/3)x + (3/2) * (14/3) = 15
6. Cancel out the fractions:
(x) + (7) = 15
7. Combine like terms:
x + 7 = 15
8. Subtract 7 from both sides to isolate x:
x = 15 - 7
9. Simplify:
x = 8
Therefore, the correct solution for x is 8. Your answer matches one of the choices given.