Solve -3x-(5/12x-17)=12x+(-4x+7/12)

$$- 3 x - ( \frac { 5 } { 12 } x - 17 ) = 12 x + ( - 4 x + \frac { 7 } { 12 } )$$

Solve for x

$$x = \frac{197}{137} = 1\frac{60}{137} \approx 1.437956204$$

Steps for Solving Linear Equation

To find the opposite of \frac{5}{12}x-17, find the opposite of each term.

$$-3x-\frac{5}{12}x-\left(-17\right)=12x-4x+\frac{7}{12}$$

The opposite of -17 is 17.

$$-3x-\frac{5}{12}x+17=12x-4x+\frac{7}{12}$$

Combine -3x and -\frac{5}{12}x to get -\frac{41}{12}x.

$$-\frac{41}{12}x+17=12x-4x+\frac{7}{12}$$

Combine 12x and -4x to get 8x.

$$-\frac{41}{12}x+17=8x+\frac{7}{12}$$

Subtract 8x from both sides.

$$-\frac{41}{12}x+17-8x=\frac{7}{12}$$

Combine -\frac{41}{12}x and -8x to get -\frac{137}{12}x.

$$-\frac{137}{12}x+17=\frac{7}{12}$$

Subtract 17 from both sides.

$$-\frac{137}{12}x=\frac{7}{12}-17$$

Convert 17 to fraction \frac{204}{12}.

$$-\frac{137}{12}x=\frac{7}{12}-\frac{204}{12}$$

Since \frac{7}{12} and \frac{204}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{137}{12}x=\frac{7-204}{12}$$

Subtract 204 from 7 to get -197.

$$-\frac{137}{12}x=-\frac{197}{12}$$

Multiply both sides by -\frac{12}{137}, the reciprocal of -\frac{137}{12}.

$$x=-\frac{197}{12}\left(-\frac{12}{137}\right)$$

Multiply -\frac{197}{12} times -\frac{12}{137} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-197\left(-12\right)}{12\times 137}$$

Do the multiplications in the fraction \frac{-197\left(-12\right)}{12\times 137}.

$$x=\frac{2364}{1644}$$

Reduce the fraction \frac{2364}{1644} to lowest terms by extracting and canceling out 12.

$$x=\frac{197}{137}$$