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

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

Solve for a

$$a=1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,4,6,2.

$$8\left(a-3\right)+3\times 3\left(a+1\right)=-2\times 5\left(1-2a\right)-6\left(a+\frac{1}{3}\right)$$

Use the distributive property to multiply 8 by a-3.

$$8a-24+3\times 3\left(a+1\right)=-2\times 5\left(1-2a\right)-6\left(a+\frac{1}{3}\right)$$

Multiply 3 and 3 to get 9.

$$8a-24+9\left(a+1\right)=-2\times 5\left(1-2a\right)-6\left(a+\frac{1}{3}\right)$$

Use the distributive property to multiply 9 by a+1.

$$8a-24+9a+9=-2\times 5\left(1-2a\right)-6\left(a+\frac{1}{3}\right)$$

Combine 8a and 9a to get 17a.

$$17a-24+9=-2\times 5\left(1-2a\right)-6\left(a+\frac{1}{3}\right)$$

Add -24 and 9 to get -15.

$$17a-15=-2\times 5\left(1-2a\right)-6\left(a+\frac{1}{3}\right)$$

Multiply -2 and 5 to get -10.

$$17a-15=-10\left(1-2a\right)-6\left(a+\frac{1}{3}\right)$$

Use the distributive property to multiply -10 by 1-2a.

$$17a-15=-10+20a-6\left(a+\frac{1}{3}\right)$$

Use the distributive property to multiply -6 by a+\frac{1}{3}.

$$17a-15=-10+20a-6a-6\times \frac{1}{3}$$

Multiply -6 and \frac{1}{3} to get \frac{-6}{3}.

$$17a-15=-10+20a-6a+\frac{-6}{3}$$

Divide -6 by 3 to get -2.

$$17a-15=-10+20a-6a-2$$

Combine 20a and -6a to get 14a.

$$17a-15=-10+14a-2$$

Subtract 2 from -10 to get -12.

$$17a-15=-12+14a$$

Subtract 14a from both sides.

$$17a-15-14a=-12$$

Combine 17a and -14a to get 3a.

$$3a-15=-12$$

Add 15 to both sides.

$$3a=-12+15$$

Add -12 and 15 to get 3.

$$3a=3$$

Divide both sides by 3.

$$a=\frac{3}{3}$$

Divide 3 by 3 to get 1.

$$a=1$$