Solve (1)/(3)(x-1)-(x-3)-(1)/(3)(x+3)+(1)/(6) | Equatix - Math Solver

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Example

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

a⋅(b-2)=3b

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

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Question

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

Evaluate

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

Solution Steps

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

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

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

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

To find the opposite of $x-3$, find the opposite of each term.

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

The opposite of $-3$ is $3$.

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

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

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

Convert $3$ to fraction $\frac{9}{3}$.

$$-\frac{2}{3}x-\frac{1}{3}+\frac{9}{3}-\frac{1}{3}\left(x+3\right)+\frac{1}{6}$$

Since $-\frac{1}{3}$ and $\frac{9}{3}$ have the same denominator, add them by adding their numerators.

$$-\frac{2}{3}x+\frac{-1+9}{3}-\frac{1}{3}\left(x+3\right)+\frac{1}{6}$$

Add $-1$ and $9$ to get $8$.

$$-\frac{2}{3}x+\frac{8}{3}-\frac{1}{3}\left(x+3\right)+\frac{1}{6}$$

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

$$-\frac{2}{3}x+\frac{8}{3}-\frac{1}{3}x-\frac{1}{3}\times 3+\frac{1}{6}$$

Cancel out $3$ and $3$.

$$-\frac{2}{3}x+\frac{8}{3}-\frac{1}{3}x-1+\frac{1}{6}$$

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

$$-x+\frac{8}{3}-1+\frac{1}{6}$$

Convert $1$ to fraction $\frac{3}{3}$.

$$-x+\frac{8}{3}-\frac{3}{3}+\frac{1}{6}$$

Since $\frac{8}{3}$ and $\frac{3}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$-x+\frac{8-3}{3}+\frac{1}{6}$$

Subtract $3$ from $8$ to get $5$.

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

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 $11$.

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

Expand

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

Solution Steps

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

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

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

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

To find the opposite of $x-3$, find the opposite of each term.

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

The opposite of $-3$ is $3$.

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

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

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

Convert $3$ to fraction $\frac{9}{3}$.

$$-\frac{2}{3}x-\frac{1}{3}+\frac{9}{3}-\frac{1}{3}\left(x+3\right)+\frac{1}{6}$$

Since $-\frac{1}{3}$ and $\frac{9}{3}$ have the same denominator, add them by adding their numerators.

$$-\frac{2}{3}x+\frac{-1+9}{3}-\frac{1}{3}\left(x+3\right)+\frac{1}{6}$$

Add $-1$ and $9$ to get $8$.

$$-\frac{2}{3}x+\frac{8}{3}-\frac{1}{3}\left(x+3\right)+\frac{1}{6}$$

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

$$-\frac{2}{3}x+\frac{8}{3}-\frac{1}{3}x-\frac{1}{3}\times 3+\frac{1}{6}$$

Cancel out $3$ and $3$.

$$-\frac{2}{3}x+\frac{8}{3}-\frac{1}{3}x-1+\frac{1}{6}$$

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

$$-x+\frac{8}{3}-1+\frac{1}{6}$$

Convert $1$ to fraction $\frac{3}{3}$.

$$-x+\frac{8}{3}-\frac{3}{3}+\frac{1}{6}$$

Since $\frac{8}{3}$ and $\frac{3}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$-x+\frac{8-3}{3}+\frac{1}{6}$$

Subtract $3$ from $8$ to get $5$.

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

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 $11$.

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