How to solve x-1=x-1/2-x-2/3

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve x-1=x-1/2-x-2/3 | Equatix

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$$x-1=x-1/2-x-2/3$$

$x=-\frac{1}{6}\approx -0.166666667$

Combine $x$ and $-x$ to get $0$.

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

Least common multiple of $2$ and $3$ is $6$. Convert $-\frac{1}{2}$ and $\frac{2}{3}$ to fractions with denominator $6$.

$$x-1=-\frac{3}{6}-\frac{4}{6}$$

Since $-\frac{3}{6}$ and $\frac{4}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$x-1=\frac{-3-4}{6}$$

Subtract $4$ from $-3$ to get $-7$.

$$x-1=-\frac{7}{6}$$

Add $1$ to both sides.

$$x=-\frac{7}{6}+1$$

Convert $1$ to fraction $\frac{6}{6}$.

$$x=-\frac{7}{6}+\frac{6}{6}$$

Since $-\frac{7}{6}$ and $\frac{6}{6}$ have the same denominator, add them by adding their numerators.

$$x=\frac{-7+6}{6}$$

Add $-7$ and $6$ to get $-1$.

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