Solve 10/9-(5x-3)=1/4x-12

$$\frac { 10 } { 9 } - ( 5 x - 3 ) = \frac { 1 } { 4 } x - 12$$

Solve for x

$$x = \frac{580}{189} = 3\frac{13}{189} \approx 3.068783069$$

Steps for Solving Linear Equation

To find the opposite of 5x-3, find the opposite of each term.

$$\frac{10}{9}-5x-\left(-3\right)=\frac{1}{4}x-12$$

The opposite of -3 is 3.

$$\frac{10}{9}-5x+3=\frac{1}{4}x-12$$

Convert 3 to fraction \frac{27}{9}.

$$\frac{10}{9}-5x+\frac{27}{9}=\frac{1}{4}x-12$$

Since \frac{10}{9} and \frac{27}{9} have the same denominator, add them by adding their numerators.

$$\frac{10+27}{9}-5x=\frac{1}{4}x-12$$

Add 10 and 27 to get 37.

$$\frac{37}{9}-5x=\frac{1}{4}x-12$$

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

$$\frac{37}{9}-5x-\frac{1}{4}x=-12$$

Combine -5x and -\frac{1}{4}x to get -\frac{21}{4}x.

$$\frac{37}{9}-\frac{21}{4}x=-12$$

Subtract \frac{37}{9} from both sides.

$$-\frac{21}{4}x=-12-\frac{37}{9}$$

Convert -12 to fraction -\frac{108}{9}.

$$-\frac{21}{4}x=-\frac{108}{9}-\frac{37}{9}$$

Since -\frac{108}{9} and \frac{37}{9} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{21}{4}x=\frac{-108-37}{9}$$

Subtract 37 from -108 to get -145.

$$-\frac{21}{4}x=-\frac{145}{9}$$

Multiply both sides by -\frac{4}{21}, the reciprocal of -\frac{21}{4}.

$$x=-\frac{145}{9}\left(-\frac{4}{21}\right)$$

Multiply -\frac{145}{9} times -\frac{4}{21} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-145\left(-4\right)}{9\times 21}$$

Do the multiplications in the fraction \frac{-145\left(-4\right)}{9\times 21}.

$$x=\frac{580}{189}$$