Solve 2/3(x-2)=1/4*(x-5)

$$\frac { 2 } { 3 } ( x - 2 ) = \frac { 1 } { 4 } \cdot ( x - 5 )$$

Solve for x

$$x=\frac{1}{5}=0.2$$

Steps for Solving Linear Equation

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

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

Express \frac{2}{3}\left(-2\right) as a single fraction.

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

Multiply 2 and -2 to get -4.

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

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

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

Use the distributive property to multiply \frac{1}{4} by x-5.

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

Multiply \frac{1}{4} and -5 to get \frac{-5}{4}.

$$\frac{2}{3}x-\frac{4}{3}=\frac{1}{4}x+\frac{-5}{4}$$

Fraction \frac{-5}{4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

$$\frac{2}{3}x-\frac{4}{3}=\frac{1}{4}x-\frac{5}{4}$$

Subtract \frac{1}{4}x from both sides.

$$\frac{2}{3}x-\frac{4}{3}-\frac{1}{4}x=-\frac{5}{4}$$

Combine \frac{2}{3}x and -\frac{1}{4}x to get \frac{5}{12}x.

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

Add \frac{4}{3} to both sides.

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

Least common multiple of 4 and 3 is 12. Convert -\frac{5}{4} and \frac{4}{3} to fractions with denominator 12.

$$\frac{5}{12}x=-\frac{15}{12}+\frac{16}{12}$$

Since -\frac{15}{12} and \frac{16}{12} have the same denominator, add them by adding their numerators.

$$\frac{5}{12}x=\frac{-15+16}{12}$$

Add -15 and 16 to get 1.

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

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

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

Multiply \frac{1}{12} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 12 in both numerator and denominator.

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