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Step-by-step Solution

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

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Answer

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

Step-by-step explanation

Problem to solve:

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

Multiply the fractions by the least common multiple of the denominators, which is $6$

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

Take $\frac{6}{2}$ out of the fraction

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

Take $\frac{-6}{3}$ out of the fraction

$3\left(x+1\right)-2\left(2-x\right)=0$
4

Solve the product $3\left(x+1\right)$

$3x+3-2\left(2-x\right)=0$
5

Solve the product $-2\left(2-x\right)$

$-1+3x+2x=0$
6

Adding $3x$ and $2x$

$5x-1=0$
7

Subtract $-1$ from both sides of the equation

$5x=1$
8

Divide both sides of the equation by $5$

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

Answer

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

Problem Analysis

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

Main topic:

Equations

Time to solve it:

~ 0.08 seconds