x+1 over 3 is equal to x over 2
pleases and thanks
2007-08-04 05:08:34 · 13 answers · asked by Sophia 1 in Science & Mathematics ➔ Mathematics
(x + 1) / 3 = x / 2
x+ 1 = 3x / 2
x + 1 = 1.5x
1 = 0.5x
x = 2
Answer: x = 2
Proof:
(2 + 1) / 3 = 2 / 2
3 / 3 = 1
1 = 1
2007-08-07 22:14:16 · answer #1 · answered by Jun Agruda 7 · 2⤊ 0⤋
Technically, there are two possible answers to your question.
Is the one over the three or are x and 1 over the three.
Since you did not use parentheses to control the order of operations, I will answer both cases. The former first.
CASE 1
x + 1/3 = x /2
2x + 2/3 = x (* Multiply the equation by 2*)
2x - x + 2/3 = 0 (* Subtract x from both sides *)
x + 2/3 = 0 (* Simplify *)
x = -2/3 (* Subtract 2/3 from each sides *)
Substitue and Check:
(-2/3) + (1/3) = (-2/3)/2
(-2/3) + (1/3) = (-1/3) [* Simplify LHS *]
(-2/3)/2 = (-2/3)*(1/2) = (-2/6) = (1/3) [* Simplify RHS *]
Good to go there.
CASE 2
(* Please ignore the character ` below. It used for spacing only *)
I want the fractions/rational expressions to look 'normal.'
(x + 1)``````` x
---------``=``----
````3```````````2
For the equation
a````c
--`=`--
b````d
The product and a & d = the product of b & c
Apply it to your problem
(x+1) * 2 = 3 * x
2x + 2 = 3x (* Distributive Property *)
2x - 3x + 2 = 3x - 3x (* Subtract 3x from each side *)
-x + 2 = 0 (* Simpify *)
-x = -2 (* Subtract 2 from each side *)
x = 2 (* Multiply each side by negative 1 *)
Substitue and Check:
2+1```````2
-----``=``---
3```````````2
3/3 =1 and 2/2 =1. Thus this x-value is the solution.
2007-08-04 05:50:57 · answer #2 · answered by marcellus 2 · 0⤊ 0⤋
x=2
2007-08-04 05:14:54 · answer #3 · answered by friend_goel 3 · 0⤊ 2⤋
(x+1)/3 is NOT x/2 !!!!
(x+1)/3 = x/3 + 1/3
2007-08-04 05:13:08 · answer #4 · answered by vlee1225 6 · 0⤊ 2⤋
Try cross multiplying (multiply the the numerator of the first side by the denominator of the second side, and multiply the numerator of the second side by the denominator of the first side)...
(x + 1) / 3 = x / 2
2(x + 1) = 3x [Multiply (x + 1) by 2 and Multiply x by 3]
2x + 2 = 3x [Distribute the 2]
2 = x [Subtract 2x from each side of the equation]
2007-08-04 05:13:38 · answer #5 · answered by ? 3 · 0⤊ 2⤋
(x + 1) / 3 = x / 2
- cross multiply
2(x + 1) = 3x
- distribute
2x + 2 = 3x
- subtract 2x from both sides
X=2
2007-08-04 05:36:50 · answer #6 · answered by Illusions 2 · 0⤊ 0⤋
its all about common denominators, whether your fractions are different due to numbers or variables.
(x+1)/3 =x/2
multiply the left by 2/2 and the right by 3/3 so the common denominator will be 6.
2(x+1)/6=3x/6
now you can disregard the denominator since it is the same on both sides. your equation becomes:
2(x+1)=3x or 2x+2=3x
add -2x to both sides.
-2x+2x+2=3x-2x or 2=x
x=2
2007-08-04 05:21:12 · answer #7 · answered by trogwolf 3 · 0⤊ 1⤋
(x + 1)/3 = x / 2
Subtract (x/2) from both sides
(x + 1)/3 - (x / 2) = 0
Multiply both sides by 6
2(x + 1) - 3x = 0
2x + 2 - 3x = 0
-x = -2
x = 2
2007-08-04 05:39:32 · answer #8 · answered by dr_no4458 4 · 0⤊ 0⤋
(x+1)/3 = x/2
Multiply by 2:
2(x+1)/3 = x
Simplify:
(2x+2)/3 = x
Multiply by 3:
(2x+2) = (3x)
Subtract 2x from both sides:
2 = x
x = 2
2007-08-04 05:16:36 · answer #9 · answered by A 4 · 0⤊ 1⤋
(x + 1) / 3 = 2
x + 1 = 6
x = 5
2007-08-04 05:47:12 · answer #10 · answered by Como 7 · 0⤊ 0⤋