Solve (x + 1) + 1/3 * (x - 1) = 5/12 * (x - 2) | Equatix - Math Solver

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Example

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

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Question

$$(x+1)+\frac{1}{3}(x-1)=\frac{5}{12}(x-2)$$

Solve for x

$x = -\frac{18}{11} = -1\frac{7}{11} \approx -1.636363636$

Steps for Solving Linear Equation

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

$$x+1+\frac{1}{3}x+\frac{1}{3}\left(-1\right)=\frac{5}{12}\left(x-2\right)$$

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

$$x+1+\frac{1}{3}x-\frac{1}{3}=\frac{5}{12}\left(x-2\right)$$

Combine $x$ and $\frac{1}{3}x$ to get $\frac{4}{3}x$.

$$\frac{4}{3}x+1-\frac{1}{3}=\frac{5}{12}\left(x-2\right)$$

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

$$\frac{4}{3}x+\frac{3}{3}-\frac{1}{3}=\frac{5}{12}\left(x-2\right)$$

Since $\frac{3}{3}$ and $\frac{1}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{3}x+\frac{3-1}{3}=\frac{5}{12}\left(x-2\right)$$

Subtract $1$ from $3$ to get $2$.

$$\frac{4}{3}x+\frac{2}{3}=\frac{5}{12}\left(x-2\right)$$

Use the distributive property to multiply $\frac{5}{12}$ by $x-2$.

$$\frac{4}{3}x+\frac{2}{3}=\frac{5}{12}x+\frac{5}{12}\left(-2\right)$$

Express $\frac{5}{12}\left(-2\right)$ as a single fraction.

$$\frac{4}{3}x+\frac{2}{3}=\frac{5}{12}x+\frac{5\left(-2\right)}{12}$$

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

$$\frac{4}{3}x+\frac{2}{3}=\frac{5}{12}x+\frac{-10}{12}$$

Reduce the fraction $\frac{-10}{12}$ to lowest terms by extracting and canceling out $2$.

$$\frac{4}{3}x+\frac{2}{3}=\frac{5}{12}x-\frac{5}{6}$$

Subtract $\frac{5}{12}x$ from both sides.

$$\frac{4}{3}x+\frac{2}{3}-\frac{5}{12}x=-\frac{5}{6}$$

Combine $\frac{4}{3}x$ and $-\frac{5}{12}x$ to get $\frac{11}{12}x$.

$$\frac{11}{12}x+\frac{2}{3}=-\frac{5}{6}$$

Subtract $\frac{2}{3}$ from both sides.

$$\frac{11}{12}x=-\frac{5}{6}-\frac{2}{3}$$

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

$$\frac{11}{12}x=-\frac{5}{6}-\frac{4}{6}$$

Since $-\frac{5}{6}$ and $\frac{4}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{12}x=\frac{-5-4}{6}$$

Subtract $4$ from $-5$ to get $-9$.

$$\frac{11}{12}x=\frac{-9}{6}$$

Reduce the fraction $\frac{-9}{6}$ to lowest terms by extracting and canceling out $3$.

$$\frac{11}{12}x=-\frac{3}{2}$$

Multiply both sides by $\frac{12}{11}$, the reciprocal of $\frac{11}{12}$.

$$x=-\frac{3}{2}\times \frac{12}{11}$$

Multiply $-\frac{3}{2}$ times $\frac{12}{11}$ by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-3\times 12}{2\times 11}$$

Do the multiplications in the fraction $\frac{-3\times 12}{2\times 11}$.

$$x=\frac{-36}{22}$$

Reduce the fraction $\frac{-36}{22}$ to lowest terms by extracting and canceling out $2$.

$$x=-\frac{18}{11}$$