(x+2)/(3) = (x+4)/(7) A. - (1)/(5) B. - (1)/(2) C. (5)/(2) D. (13)/(2)

Question

`(x+2)/(3) = (x+4)/(7)`

A.
`- (1)/(5)`
B. -
`(1)/(2)`
C.
`(5)/(2)`
D.
`(13)/(2)`

Answer 1

It’s -1/2

Firstly: simplify the equation using cross multiplication: 7(x+2)=3(x+4)

Secondly: distribute 7 and 3 through the parentheses: 7x+14=3x+12

Thirdly: move the variables to the left hand side and change its sign: 7x-3x+14=12, and then move the constant to the right hand side and change its sign: 7x-3x=12-14 and solve both sides

Fourthly: collect like terms (the x variables): 4x=12-14 then calculate the difference on the right side: 4x=-2

Fifth: divide both sides of the equation by 4: x=-1/2

ANSWER: x=-1/2

Answer 2

x = (-1)/2 thus B is your answer (-1/2= (-1)/2) are the same

Explanation:

Solve for x:

(x + 2)/3 = (x + 4)/7

Multiply both sides by 21:

(21 (x + 2))/3 = (21 (x + 4))/7

21/3 = (3×7)/3 = 7:

7 (x + 2) = (21 (x + 4))/7

21/7 = (7×3)/7 = 3:

7 (x + 2) = 3 (x + 4)

Expand out terms of the left hand side:

7 x + 14 = 3 (x + 4)

Expand out terms of the right hand side:

7 x + 14 = 3 x + 12

Subtract 3 x from both sides:

(7 x - 3 x) + 14 = (3 x - 3 x) + 12

7 x - 3 x = 4 x:

4 x + 14 = (3 x - 3 x) + 12

3 x - 3 x = 0:

4 x + 14 = 12

Subtract 14 from both sides:

4 x + (14 - 14) = 12 - 14

14 - 14 = 0:

4 x = 12 - 14

12 - 14 = -2:

4 x = -2

Divide both sides of 4 x = -2 by 4:

(4 x)/4 = (-2)/4

4/4 = 1:

x = (-2)/4

The gcd of -2 and 4 is 2, so (-2)/4 = (2 (-1))/(2×2) = 2/2×(-1)/2 = (-1)/2:

Answer: x = (-1)/2