Step-by-step Solution

Solve the equation $\frac{x+1}{2}-\left(\frac{2-x}{3}\right)=0$

Go!
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Final Answer

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

Step-by-step explanation

Problem to solve:

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

Multiplying the fraction by $-1$

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

Take $\frac{-1}{3}$ out of the fraction

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

Solve the product $-\frac{1}{3}\left(2-x\right)$

$\frac{x+1}{2}-\frac{2}{3}+\frac{1}{3}x=0$
4

Moving the term $-\frac{2}{3}$ to the other side of the equation with opposite sign

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

Combine $\frac{x+1}{2}+\frac{1}{3}x$ in a single fraction

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

Adding $\frac{2}{3}x$ and $x$

$\frac{x\left(\frac{2}{3}+1\right)+1}{2}=\frac{2}{3}$
7

Add the values $\frac{2}{3}$ and $1$

$\frac{\frac{5}{3}x+1}{2}=\frac{2}{3}$
8

Multiply both sides of the equation by $2$

$\frac{5}{3}x+1=\frac{4}{3}$
9

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

$\frac{5}{3}x=\frac{1}{3}$
10

Divide both sides of the equation by $\frac{5}{3}$

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

Final Answer

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

Problem Analysis

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

Main topic:

Equations

Time to solve it:

~ 0.04 seconds