Solve x-3/17(2x-1)=7/34(1-2x)+10x-3/2

$$x - \frac { 3 } { 17 } ( 2 x - 1 ) = \frac { 7 } { 34 } ( 1 - 2 x ) + \frac { 10 x - 3 } { 2 }$$

Solve for x

$$x=\frac{25}{67}\approx 0.373134328$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 34, the least common multiple of 17,34,2.

$$34x-6\left(2x-1\right)=7\left(1-2x\right)+17\left(10x-3\right)$$

Use the distributive property to multiply -6 by 2x-1.

$$34x-12x+6=7\left(1-2x\right)+17\left(10x-3\right)$$

Combine 34x and -12x to get 22x.

$$22x+6=7\left(1-2x\right)+17\left(10x-3\right)$$

Use the distributive property to multiply 7 by 1-2x.

$$22x+6=7-14x+17\left(10x-3\right)$$

Use the distributive property to multiply 17 by 10x-3.

$$22x+6=7-14x+170x-51$$

Combine -14x and 170x to get 156x.

$$22x+6=7+156x-51$$

Subtract 51 from 7 to get -44.

$$22x+6=-44+156x$$

Subtract 156x from both sides.

$$22x+6-156x=-44$$

Combine 22x and -156x to get -134x.

$$-134x+6=-44$$

Subtract 6 from both sides.

$$-134x=-44-6$$

Subtract 6 from -44 to get -50.

$$-134x=-50$$

Divide both sides by -134.

$$x=\frac{-50}{-134}$$

Reduce the fraction \frac{-50}{-134} to lowest terms by extracting and canceling out -2.

$$x=\frac{25}{67}$$