Solve -x/6-3(x+2)/5-4(2x+1)/15=3(3x+2)/10-frac{4}{3}

$$- \frac { x } { 6 } - \frac { 3 ( x + 2 ) } { 5 } - \frac { 4 ( 2 x + 1 ) } { 15 } = \frac { 3 ( 3 x + 2 ) } { 10 } - \frac { 4 } { 3 }$$

Solve for x

$$x=-\frac{1}{3}\approx -0.333333333$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 6,5,15,10,3.

$$-5x-6\times 3\left(x+2\right)-2\times 4\left(2x+1\right)=3\times 3\left(3x+2\right)-40$$

Multiply -6 and 3 to get -18.

$$-5x-18\left(x+2\right)-2\times 4\left(2x+1\right)=3\times 3\left(3x+2\right)-40$$

Use the distributive property to multiply -18 by x+2.

$$-5x-18x-36-2\times 4\left(2x+1\right)=3\times 3\left(3x+2\right)-40$$

Combine -5x and -18x to get -23x.

$$-23x-36-2\times 4\left(2x+1\right)=3\times 3\left(3x+2\right)-40$$

Multiply -2 and 4 to get -8.

$$-23x-36-8\left(2x+1\right)=3\times 3\left(3x+2\right)-40$$

Use the distributive property to multiply -8 by 2x+1.

$$-23x-36-16x-8=3\times 3\left(3x+2\right)-40$$

Combine -23x and -16x to get -39x.

$$-39x-36-8=3\times 3\left(3x+2\right)-40$$

Subtract 8 from -36 to get -44.

$$-39x-44=3\times 3\left(3x+2\right)-40$$

Multiply 3 and 3 to get 9.

$$-39x-44=9\left(3x+2\right)-40$$

Use the distributive property to multiply 9 by 3x+2.

$$-39x-44=27x+18-40$$

Subtract 40 from 18 to get -22.

$$-39x-44=27x-22$$

Subtract 27x from both sides.

$$-39x-44-27x=-22$$

Combine -39x and -27x to get -66x.

$$-66x-44=-22$$

Add 44 to both sides.

$$-66x=-22+44$$

Add -22 and 44 to get 22.

$$-66x=22$$

Divide both sides by -66.

$$x=\frac{22}{-66}$$

Reduce the fraction \frac{22}{-66} to lowest terms by extracting and canceling out 22.

$$x=-\frac{1}{3}$$