# Solve the equation (x+1)/2-1(2-1x)/3=0

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

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

## Step by step solution

Problem

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

Multiply the fractions by the least common multiple of the denominators

$lcm\left(2,3\right)\frac{1+x}{2}-1\cdot lcm\left(2,3\right)\left(\frac{2-x}{3}\right)=0\cdot lcm\left(2,3\right)$
2

Any expression multiplied by $0$ is equal to $0$

$lcm\left(2,3\right)\frac{1+x}{2}-1\cdot lcm\left(2,3\right)\left(\frac{2-x}{3}\right)=0$
3

Apply the formula: $lcm\left(a,b\right)$, where $a=2$ and $b=3$

$6\frac{1+x}{2}-1\cdot 6\left(\frac{2-x}{3}\right)=0$
4

Multiply $6$ times $-1$

$6\frac{1+x}{2}-6\frac{2-x}{3}=0$
5

Simplify the fraction

$3\left(1+x\right)-2\left(2-x\right)=0$
6

Multiply $\left(x+1\right)$ by $3$

$2x-4+3+3x=0$
7

Subtract the values $3$ and $-4$

$2x+3x-1=0$
8

Adding $3x$ and $2x$

$5x-1=0$
9

Subtract $-1$ from both sides of the equation

$5x=1$
10

Multiply both sides of the equation by 

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

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

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