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# Solve the equation $\frac{x+1}{2}-\frac{2-x}{3}=0$

## Step-by-step Solution

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### Videos

$x=\frac{1}{5}$
Got another answer? Verify it here

## Step-by-step Solution

Problem to solve:

$\frac{x+1}{2}-\frac{2-x}{3}=0$

Choose the solving method

1

Solve the product $-(2-x)$

$\frac{x+1}{2}+\frac{-2+x}{3}=0$
2

The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors

$L.C.M.=3\cdot 2=6$
3

Obtained the least common multiple, we place the LCM as the denominator of each fraction and in the numerator of each fraction we add the factors that we need to complete

$\frac{3\left(x+1\right)}{6}+\frac{2\left(-2+x\right)}{6}$
4

Simplify the numerators

$\frac{3x+3}{6}+\frac{-4+2x}{6}$

Subtract the values $3$ and $-4$

$\frac{-1+3x+2x}{6}=0$

Combining like terms $3x$ and $2x$

$\frac{-1+5x}{6}=0$
5

Combine and simplify all terms in the same fraction with common denominator $6$

$\frac{-1+5x}{6}=0$
6

Multiply both sides of the equation by $6$

$-1+5x=0$
7

We need to isolate the dependent variable $x$, we can do that by subtracting $-1$ from both sides of the equation

$5x=1$
8

Eliminate the $5$ from the left side, multiplying both sides of the equation by the inverse of $5$

$x=\frac{1}{5}$

$x=\frac{1}{5}$
SnapXam A2

### beta Got another answer? Verify it!

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

$\frac{x+1}{2}-\frac{2-x}{3}=0$

### Main topic:

One-variable linear equations

~ 0.07 s