How to solve x+1/2-3=2x-2/3+4

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+1/2-3=2x-2/3+4 | Equatix

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Question

$$x+1/2-3=2x-2/3+4$$

Solve for x

$x = -\frac{35}{6} = -5\frac{5}{6} \approx -5.833333333$

Steps for Solving Linear Equation

Convert $3$ to fraction $\frac{6}{2}$.

$$x+\frac{1}{2}-\frac{6}{2}=2x-\frac{2}{3}+4$$

Since $\frac{1}{2}$ and $\frac{6}{2}$ have the same denominator, subtract them by subtracting their numerators.

$$x+\frac{1-6}{2}=2x-\frac{2}{3}+4$$

Subtract $6$ from $1$ to get $-5$.

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

Convert $4$ to fraction $\frac{12}{3}$.

$$x-\frac{5}{2}=2x-\frac{2}{3}+\frac{12}{3}$$

Since $-\frac{2}{3}$ and $\frac{12}{3}$ have the same denominator, add them by adding their numerators.

$$x-\frac{5}{2}=2x+\frac{-2+12}{3}$$

Add $-2$ and $12$ to get $10$.

$$x-\frac{5}{2}=2x+\frac{10}{3}$$

Subtract $2x$ from both sides.

$$x-\frac{5}{2}-2x=\frac{10}{3}$$

Combine $x$ and $-2x$ to get $-x$.

$$-x-\frac{5}{2}=\frac{10}{3}$$

Add $\frac{5}{2}$ to both sides.

$$-x=\frac{10}{3}+\frac{5}{2}$$

Least common multiple of $3$ and $2$ is $6$. Convert $\frac{10}{3}$ and $\frac{5}{2}$ to fractions with denominator $6$.

$$-x=\frac{20}{6}+\frac{15}{6}$$

Since $\frac{20}{6}$ and $\frac{15}{6}$ have the same denominator, add them by adding their numerators.

$$-x=\frac{20+15}{6}$$

Add $20$ and $15$ to get $35$.

$$-x=\frac{35}{6}$$

Multiply both sides by $-1$.

$$x=-\frac{35}{6}$$

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