Solve 1 4 (x-2)= 1 5 (x-1)= | 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

$$\frac{1}{4}(x-2)=\frac{1}{5}(x-1)=$$

Solve for x

$x=6$

Steps for Solving Linear Equation

Use the distributive property to multiply $\frac{1}{4}$ by $x-2$.

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

Multiply $\frac{1}{4}$ and $-2$ to get $\frac{-2}{4}$.

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

Reduce the fraction $\frac{-2}{4}$ to lowest terms by extracting and canceling out $2$.

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

Use the distributive property to multiply $\frac{1}{5}$ by $x-1$.

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

Multiply $\frac{1}{5}$ and $-1$ to get $-\frac{1}{5}$.

$$\frac{1}{4}x-\frac{1}{2}=\frac{1}{5}x-\frac{1}{5}$$

Subtract $\frac{1}{5}x$ from both sides.

$$\frac{1}{4}x-\frac{1}{2}-\frac{1}{5}x=-\frac{1}{5}$$

Combine $\frac{1}{4}x$ and $-\frac{1}{5}x$ to get $\frac{1}{20}x$.

$$\frac{1}{20}x-\frac{1}{2}=-\frac{1}{5}$$

Add $\frac{1}{2}$ to both sides.

$$\frac{1}{20}x=-\frac{1}{5}+\frac{1}{2}$$

Least common multiple of $5$ and $2$ is $10$. Convert $-\frac{1}{5}$ and $\frac{1}{2}$ to fractions with denominator $10$.

$$\frac{1}{20}x=-\frac{2}{10}+\frac{5}{10}$$

Since $-\frac{2}{10}$ and $\frac{5}{10}$ have the same denominator, add them by adding their numerators.

$$\frac{1}{20}x=\frac{-2+5}{10}$$

Add $-2$ and $5$ to get $3$.

$$\frac{1}{20}x=\frac{3}{10}$$

Multiply both sides by $20$, the reciprocal of $\frac{1}{20}$.

$$x=\frac{3}{10}\times 20$$

Express $\frac{3}{10}\times 20$ as a single fraction.

$$x=\frac{3\times 20}{10}$$

Multiply $3$ and $20$ to get $60$.

$$x=\frac{60}{10}$$

Divide $60$ by $10$ to get $6$.

$$x=6$$