Solve 2(3x-2)+5(3/2x-2)-1/15=6x/5-3/5-2-frac{49}{15}

$$2 ( 3 x - 2 ) + 5 ( \frac { 3 } { 2 } x - 2 ) - \frac { 1 } { 15 } = \frac { 6 x } { 5 } - \frac { 3 } { 5 } - 2 - \frac { 49 } { 15 }$$

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 2,15,5.

$$60\left(3x-2\right)+150\left(\frac{3}{2}x-2\right)-2=6\times 6x-18-60-98$$

Use the distributive property to multiply 60 by 3x-2.

$$180x-120+150\left(\frac{3}{2}x-2\right)-2=6\times 6x-18-60-98$$

Use the distributive property to multiply 150 by \frac{3}{2}x-2.

$$180x-120+150\times \frac{3}{2}x-300-2=6\times 6x-18-60-98$$

Express 150\times \frac{3}{2} as a single fraction.

$$180x-120+\frac{150\times 3}{2}x-300-2=6\times 6x-18-60-98$$

Multiply 150 and 3 to get 450.

$$180x-120+\frac{450}{2}x-300-2=6\times 6x-18-60-98$$

Divide 450 by 2 to get 225.

$$180x-120+225x-300-2=6\times 6x-18-60-98$$

Combine 180x and 225x to get 405x.

$$405x-120-300-2=6\times 6x-18-60-98$$

Subtract 300 from -120 to get -420.

$$405x-420-2=6\times 6x-18-60-98$$

Subtract 2 from -420 to get -422.

$$405x-422=6\times 6x-18-60-98$$

Multiply 6 and 6 to get 36.

$$405x-422=36x-18-60-98$$

Subtract 60 from -18 to get -78.

$$405x-422=36x-78-98$$

Subtract 98 from -78 to get -176.

$$405x-422=36x-176$$

Subtract 36x from both sides.

$$405x-422-36x=-176$$

Combine 405x and -36x to get 369x.

$$369x-422=-176$$

Add 422 to both sides.

$$369x=-176+422$$

Add -176 and 422 to get 246.

$$369x=246$$

Divide both sides by 369.

$$x=\frac{246}{369}$$

Reduce the fraction \frac{246}{369} to lowest terms by extracting and canceling out 123.

$$x=\frac{2}{3}$$