Solve 143/144=a+b+a+frac{d/6/4/3}{2}

$$\frac { 143 } { 144 } = \frac { a + \frac { b + \frac { a + \frac { d } { 6 } } { 4 } } { 3 } } { 2 }$$

Solve for a

$$a=-\frac{d}{78}-\frac{4b}{13}+\frac{11}{6}$$

Steps for Solving Linear Equation

Multiply both sides by 2.

$$\frac{143}{144}\times 2=a+\frac{b+\frac{a+\frac{d}{6}}{4}}{3}$$

Multiply both sides of the equation by 144, the least common multiple of 144,3.

$$143\times 2=144a+48\left(b+\frac{a+\frac{d}{6}}{4}\right)$$

Multiply 143 and 2 to get 286.

$$286=144a+48\left(b+\frac{a+\frac{d}{6}}{4}\right)$$

Use the distributive property to multiply 48 by b+\frac{a+\frac{d}{6}}{4}.

$$286=144a+48b+48\times \frac{a+\frac{d}{6}}{4}$$

Swap sides so that all variable terms are on the left hand side.

$$144a+48b+48\times \frac{a+\frac{d}{6}}{4}=286$$

Subtract 48b from both sides.

$$144a+48\times \frac{a+\frac{d}{6}}{4}=286-48b$$

Multiply both sides of the equation by 4.

$$576a+48\left(a+\frac{d}{6}\right)=1144-192b$$

Multiply both sides of the equation by 6.

$$3456a+288\left(a+\frac{d}{6}\right)=6864-1152b$$

Use the distributive property to multiply 288 by a+\frac{d}{6}.

$$3456a+288a+288\times \frac{d}{6}=6864-1152b$$

Cancel out 6, the greatest common factor in 288 and 6.

$$3456a+288a+48d=6864-1152b$$

Combine 3456a and 288a to get 3744a.

$$3744a+48d=6864-1152b$$

Subtract 48d from both sides.

$$3744a=6864-1152b-48d$$

The equation is in standard form.

$$3744a=6864-48d-1152b$$

Divide both sides by 3744.

$$\frac{3744a}{3744}=\frac{6864-48d-1152b}{3744}$$

Dividing by 3744 undoes the multiplication by 3744.

$$a=\frac{6864-48d-1152b}{3744}$$

Divide 6864-1152b-48d by 3744.

$$a=-\frac{d}{78}-\frac{4b}{13}+\frac{11}{6}$$

Solve for b

$$b=-\frac{d}{24}-\frac{13a}{4}+\frac{143}{24}$$

Steps for Solving Linear Equation

Multiply both sides by 2.

$$\frac{143}{144}\times 2=a+\frac{b+\frac{a+\frac{d}{6}}{4}}{3}$$

Multiply both sides of the equation by 144, the least common multiple of 144,3.

$$143\times 2=144a+48\left(b+\frac{a+\frac{d}{6}}{4}\right)$$

Multiply 143 and 2 to get 286.

$$286=144a+48\left(b+\frac{a+\frac{d}{6}}{4}\right)$$

Use the distributive property to multiply 48 by b+\frac{a+\frac{d}{6}}{4}.

$$286=144a+48b+48\times \frac{a+\frac{d}{6}}{4}$$

Swap sides so that all variable terms are on the left hand side.

$$144a+48b+48\times \frac{a+\frac{d}{6}}{4}=286$$

Subtract 144a from both sides.

$$48b+48\times \frac{a+\frac{d}{6}}{4}=286-144a$$

Subtract 48\times \frac{a+\frac{d}{6}}{4} from both sides.

$$48b=286-144a-48\times \frac{a+\frac{d}{6}}{4}$$

Multiply both sides of the equation by 4.

$$192b=4\left(286-144a\right)-48\left(a+\frac{d}{6}\right)$$

Multiply both sides of the equation by 6.

$$1152b=24\left(286-144a\right)-6\times 48\left(a+\frac{d}{6}\right)$$

Use the distributive property to multiply 24 by 286-144a.

$$1152b=6864-3456a-6\times 48\left(a+\frac{d}{6}\right)$$

Multiply -6 and 48 to get -288.

$$1152b=6864-3456a-288\left(a+\frac{d}{6}\right)$$

Use the distributive property to multiply -288 by a+\frac{d}{6}.

$$1152b=6864-3456a-288a-288\times \frac{d}{6}$$

Cancel out 6, the greatest common factor in 288 and 6.

$$1152b=6864-3456a-288a-48d$$

Combine -3456a and -288a to get -3744a.

$$1152b=6864-3744a-48d$$

The equation is in standard form.

$$1152b=6864-48d-3744a$$

Divide both sides by 1152.

$$\frac{1152b}{1152}=\frac{6864-48d-3744a}{1152}$$

Dividing by 1152 undoes the multiplication by 1152.

$$b=\frac{6864-48d-3744a}{1152}$$

Divide 6864-3744a-48d by 1152.

$$b=-\frac{d}{24}-\frac{13a}{4}+\frac{143}{24}$$