Solve 5x-3/7-2x-1/14-3x-4/3=2x-3/21+frac{3x-4}{10}

$$\frac { 5 x - 3 } { 7 } - \frac { 2 x - 1 } { 14 } - \frac { 3 x - 4 } { 3 } = \frac { 2 x - 3 } { 21 } + \frac { 3 x - 4 } { 10 }$$

Solve for x

$$x = \frac{319}{173} = 1\frac{146}{173} \approx 1.843930636$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 210, the least common multiple of 7,14,3,21,10.

$$30\left(5x-3\right)-15\left(2x-1\right)-70\left(3x-4\right)=10\left(2x-3\right)+21\left(3x-4\right)$$

Use the distributive property to multiply 30 by 5x-3.

$$150x-90-15\left(2x-1\right)-70\left(3x-4\right)=10\left(2x-3\right)+21\left(3x-4\right)$$

Use the distributive property to multiply -15 by 2x-1.

$$150x-90-30x+15-70\left(3x-4\right)=10\left(2x-3\right)+21\left(3x-4\right)$$

Combine 150x and -30x to get 120x.

$$120x-90+15-70\left(3x-4\right)=10\left(2x-3\right)+21\left(3x-4\right)$$

Add -90 and 15 to get -75.

$$120x-75-70\left(3x-4\right)=10\left(2x-3\right)+21\left(3x-4\right)$$

Use the distributive property to multiply -70 by 3x-4.

$$120x-75-210x+280=10\left(2x-3\right)+21\left(3x-4\right)$$

Combine 120x and -210x to get -90x.

$$-90x-75+280=10\left(2x-3\right)+21\left(3x-4\right)$$

Add -75 and 280 to get 205.

$$-90x+205=10\left(2x-3\right)+21\left(3x-4\right)$$

Use the distributive property to multiply 10 by 2x-3.

$$-90x+205=20x-30+21\left(3x-4\right)$$

Use the distributive property to multiply 21 by 3x-4.

$$-90x+205=20x-30+63x-84$$

Combine 20x and 63x to get 83x.

$$-90x+205=83x-30-84$$

Subtract 84 from -30 to get -114.

$$-90x+205=83x-114$$

Subtract 83x from both sides.

$$-90x+205-83x=-114$$

Combine -90x and -83x to get -173x.

$$-173x+205=-114$$

Subtract 205 from both sides.

$$-173x=-114-205$$

Subtract 205 from -114 to get -319.

$$-173x=-319$$

Divide both sides by -173.

$$x=\frac{-319}{-173}$$

Fraction \frac{-319}{-173} can be simplified to \frac{319}{173} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{319}{173}$$