Solve 3/5x-4-1/3left(2x-9right)=1/4left(x-1right)-2

$$\frac{ 3 }{ 5 } x-4- \frac{ 1 }{ 3 } \left( 2x-9 \right) = \frac{ 1 }{ 4 } \left( x-1 \right) -2$$

Solve for x

$$x = \frac{75}{19} = 3\frac{18}{19} \approx 3.947368421$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{1}{3} by 2x-9.

$$\frac{3}{5}x-4-\frac{1}{3}\times 2x-\frac{1}{3}\left(-9\right)=\frac{1}{4}\left(x-1\right)-2$$

Express -\frac{1}{3}\times 2 as a single fraction.

$$\frac{3}{5}x-4+\frac{-2}{3}x-\frac{1}{3}\left(-9\right)=\frac{1}{4}\left(x-1\right)-2$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\frac{3}{5}x-4-\frac{2}{3}x-\frac{1}{3}\left(-9\right)=\frac{1}{4}\left(x-1\right)-2$$

Express -\frac{1}{3}\left(-9\right) as a single fraction.

$$\frac{3}{5}x-4-\frac{2}{3}x+\frac{-\left(-9\right)}{3}=\frac{1}{4}\left(x-1\right)-2$$

Multiply -1 and -9 to get 9.

$$\frac{3}{5}x-4-\frac{2}{3}x+\frac{9}{3}=\frac{1}{4}\left(x-1\right)-2$$

Divide 9 by 3 to get 3.

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

Combine \frac{3}{5}x and -\frac{2}{3}x to get -\frac{1}{15}x.

$$-\frac{1}{15}x-4+3=\frac{1}{4}\left(x-1\right)-2$$

Add -4 and 3 to get -1.

$$-\frac{1}{15}x-1=\frac{1}{4}\left(x-1\right)-2$$

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

$$-\frac{1}{15}x-1=\frac{1}{4}x+\frac{1}{4}\left(-1\right)-2$$

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

$$-\frac{1}{15}x-1=\frac{1}{4}x-\frac{1}{4}-2$$

Convert 2 to fraction \frac{8}{4}.

$$-\frac{1}{15}x-1=\frac{1}{4}x-\frac{1}{4}-\frac{8}{4}$$

Since -\frac{1}{4} and \frac{8}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{15}x-1=\frac{1}{4}x+\frac{-1-8}{4}$$

Subtract 8 from -1 to get -9.

$$-\frac{1}{15}x-1=\frac{1}{4}x-\frac{9}{4}$$

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

$$-\frac{1}{15}x-1-\frac{1}{4}x=-\frac{9}{4}$$

Combine -\frac{1}{15}x and -\frac{1}{4}x to get -\frac{19}{60}x.

$$-\frac{19}{60}x-1=-\frac{9}{4}$$

Add 1 to both sides.

$$-\frac{19}{60}x=-\frac{9}{4}+1$$

Convert 1 to fraction \frac{4}{4}.

$$-\frac{19}{60}x=-\frac{9}{4}+\frac{4}{4}$$

Since -\frac{9}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$-\frac{19}{60}x=\frac{-9+4}{4}$$

Add -9 and 4 to get -5.

$$-\frac{19}{60}x=-\frac{5}{4}$$

Multiply both sides by -\frac{60}{19}, the reciprocal of -\frac{19}{60}.

$$x=-\frac{5}{4}\left(-\frac{60}{19}\right)$$

Multiply -\frac{5}{4} times -\frac{60}{19} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-5\left(-60\right)}{4\times 19}$$

Do the multiplications in the fraction \frac{-5\left(-60\right)}{4\times 19}.

$$x=\frac{300}{76}$$

Reduce the fraction \frac{300}{76} to lowest terms by extracting and canceling out 4.

$$x=\frac{75}{19}$$