Solve 1/2 * (x + 1) + 1/3 * (x - 1) = 5/12 * (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

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

Solve for x

$x = -\frac{12}{5} = -2\frac{2}{5} = -2.4$

Steps for Solving Linear Equation

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

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

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

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

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

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

Combine $\frac{1}{2}x$ and $\frac{1}{3}x$ to get $\frac{5}{6}x$.

$$\frac{5}{6}x+\frac{1}{2}-\frac{1}{3}=\frac{5}{12}\left(x-2\right)$$

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

$$\frac{5}{6}x+\frac{3}{6}-\frac{2}{6}=\frac{5}{12}\left(x-2\right)$$

Since $\frac{3}{6}$ and $\frac{2}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}x+\frac{3-2}{6}=\frac{5}{12}\left(x-2\right)$$

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

$$\frac{5}{6}x+\frac{1}{6}=\frac{5}{12}\left(x-2\right)$$

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

$$\frac{5}{6}x+\frac{1}{6}=\frac{5}{12}x+\frac{5}{12}\left(-2\right)$$

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

$$\frac{5}{6}x+\frac{1}{6}=\frac{5}{12}x+\frac{5\left(-2\right)}{12}$$

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

$$\frac{5}{6}x+\frac{1}{6}=\frac{5}{12}x+\frac{-10}{12}$$

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

$$\frac{5}{6}x+\frac{1}{6}=\frac{5}{12}x-\frac{5}{6}$$

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

$$\frac{5}{6}x+\frac{1}{6}-\frac{5}{12}x=-\frac{5}{6}$$

Combine $\frac{5}{6}x$ and $-\frac{5}{12}x$ to get $\frac{5}{12}x$.

$$\frac{5}{12}x+\frac{1}{6}=-\frac{5}{6}$$

Subtract $\frac{1}{6}$ from both sides.

$$\frac{5}{12}x=-\frac{5}{6}-\frac{1}{6}$$

Since $-\frac{5}{6}$ and $\frac{1}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{12}x=\frac{-5-1}{6}$$

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

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

Divide $-6$ by $6$ to get $-1$.

$$\frac{5}{12}x=-1$$

Multiply both sides by $\frac{12}{5}$, the reciprocal of $\frac{5}{12}$.

$$x=-\frac{12}{5}$$