Solve Date Page 1/3 * (x - 2) - 1/2 * (x - 1) = 5/6 * (x + 2) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac { 1 } { 3 } ( x - 2 ) - \frac { 1 } { 2 } ( x - 1 ) = \frac { 5 } { 6 } ( x + 2 )$$

Solve for x

$x = -\frac{11}{6} = -1\frac{5}{6} \approx -1.833333333$

Steps for Solving Linear Equation

Use the distributive property to multiply $\frac{1}{3}$ by $x-2$.

$$\frac{1}{3}x+\frac{1}{3}\left(-2\right)-\frac{1}{2}\left(x-1\right)=\frac{5}{6}\left(x+2\right)$$

Multiply $\frac{1}{3}$ and $-2$ to get $\frac{-2}{3}$.

$$\frac{1}{3}x+\frac{-2}{3}-\frac{1}{2}\left(x-1\right)=\frac{5}{6}\left(x+2\right)$$

Fraction $\frac{-2}{3}$ can be rewritten as $-\frac{2}{3}$ by extracting the negative sign.

$$\frac{1}{3}x-\frac{2}{3}-\frac{1}{2}\left(x-1\right)=\frac{5}{6}\left(x+2\right)$$

Use the distributive property to multiply $-\frac{1}{2}$ by $x-1$.

$$\frac{1}{3}x-\frac{2}{3}-\frac{1}{2}x-\frac{1}{2}\left(-1\right)=\frac{5}{6}\left(x+2\right)$$

Multiply $-\frac{1}{2}$ and $-1$ to get $\frac{1}{2}$.

$$\frac{1}{3}x-\frac{2}{3}-\frac{1}{2}x+\frac{1}{2}=\frac{5}{6}\left(x+2\right)$$

Combine $\frac{1}{3}x$ and $-\frac{1}{2}x$ to get $-\frac{1}{6}x$.

$$-\frac{1}{6}x-\frac{2}{3}+\frac{1}{2}=\frac{5}{6}\left(x+2\right)$$

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

$$-\frac{1}{6}x-\frac{4}{6}+\frac{3}{6}=\frac{5}{6}\left(x+2\right)$$

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

$$-\frac{1}{6}x+\frac{-4+3}{6}=\frac{5}{6}\left(x+2\right)$$

Add $-4$ and $3$ to get $-1$.

$$-\frac{1}{6}x-\frac{1}{6}=\frac{5}{6}\left(x+2\right)$$

Use the distributive property to multiply $\frac{5}{6}$ by $x+2$.

$$-\frac{1}{6}x-\frac{1}{6}=\frac{5}{6}x+\frac{5}{6}\times 2$$

Express $\frac{5}{6}\times 2$ as a single fraction.

$$-\frac{1}{6}x-\frac{1}{6}=\frac{5}{6}x+\frac{5\times 2}{6}$$

Multiply $5$ and $2$ to get $10$.

$$-\frac{1}{6}x-\frac{1}{6}=\frac{5}{6}x+\frac{10}{6}$$

Reduce the fraction $\frac{10}{6}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{1}{6}x-\frac{1}{6}=\frac{5}{6}x+\frac{5}{3}$$

Subtract $\frac{5}{6}x$ from both sides.

$$-\frac{1}{6}x-\frac{1}{6}-\frac{5}{6}x=\frac{5}{3}$$

Combine $-\frac{1}{6}x$ and $-\frac{5}{6}x$ to get $-x$.

$$-x-\frac{1}{6}=\frac{5}{3}$$

Add $\frac{1}{6}$ to both sides.

$$-x=\frac{5}{3}+\frac{1}{6}$$

Least common multiple of $3$ and $6$ is $6$. Convert $\frac{5}{3}$ and $\frac{1}{6}$ to fractions with denominator $6$.

$$-x=\frac{10}{6}+\frac{1}{6}$$

Since $\frac{10}{6}$ and $\frac{1}{6}$ have the same denominator, add them by adding their numerators.

$$-x=\frac{10+1}{6}$$

Add $10$ and $1$ to get $11$.

$$-x=\frac{11}{6}$$

Multiply both sides by $-1$.

$$x=-\frac{11}{6}$$