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Exercise

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

Step-by-step Solution

1

Simplify 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 (LCM), we place it 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

$\frac{3x+3}{6}+\frac{-4+2x}{6}$
5

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

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

Multiply both sides of the equation by $6$

$5x-1=0$
7

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

$5x-1+1=0+1$
8

Canceling terms on both sides

$5x=1$
9

Divide both sides of the equation by $5$

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

Final answer to the exercise

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

Exact Numeric Answer

$x=0.2$

Try other ways to solve this exercise

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  • Solve for x
  • Find the derivative using the definition
  • Solve by quadratic formula (general formula)
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  • Find the integral
  • Find the derivative
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  • Factor by completing the square
  • Find the roots
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