Solve 5/4(x-4)=4/6(x-3)

$$\frac{ 5 }{ 4 } (x-4)= \frac{ 4 }{ 6 } (x-3)$$

Solve for x

$$x = \frac{36}{7} = 5\frac{1}{7} \approx 5.142857143$$

Steps for Solving Linear Equation

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

$$\frac{5}{4}x+\frac{5}{4}\left(-4\right)=\frac{4}{6}\left(x-3\right)$$

Express \frac{5}{4}\left(-4\right) as a single fraction.

$$\frac{5}{4}x+\frac{5\left(-4\right)}{4}=\frac{4}{6}\left(x-3\right)$$

Multiply 5 and -4 to get -20.

$$\frac{5}{4}x+\frac{-20}{4}=\frac{4}{6}\left(x-3\right)$$

Divide -20 by 4 to get -5.

$$\frac{5}{4}x-5=\frac{4}{6}\left(x-3\right)$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

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

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

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

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

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

Multiply 2 and -3 to get -6.

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

Divide -6 by 3 to get -2.

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

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

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

Combine \frac{5}{4}x and -\frac{2}{3}x to get \frac{7}{12}x.

$$\frac{7}{12}x-5=-2$$

Add 5 to both sides.

$$\frac{7}{12}x=-2+5$$

Add -2 and 5 to get 3.

$$\frac{7}{12}x=3$$

Multiply both sides by \frac{12}{7}, the reciprocal of \frac{7}{12}.

$$x=3\times \frac{12}{7}$$

Express 3\times \frac{12}{7} as a single fraction.

$$x=\frac{3\times 12}{7}$$

Multiply 3 and 12 to get 36.

$$x=\frac{36}{7}$$