Solve 4(x/3+x/5)-7(x/6+x/15)=3

$$4 ( \frac { x } { 3 } + \frac { x } { 5 } ) - 7 ( \frac { x } { 6 } + \frac { x } { 15 } ) = 3$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

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

$$120\left(\frac{x}{3}+\frac{x}{5}\right)-210\left(\frac{x}{6}+\frac{x}{15}\right)=90$$

Combine \frac{x}{3} and \frac{x}{5} to get \frac{8}{15}x.

$$120\times \frac{8}{15}x-210\left(\frac{x}{6}+\frac{x}{15}\right)=90$$

Express 120\times \frac{8}{15} as a single fraction.

$$\frac{120\times 8}{15}x-210\left(\frac{x}{6}+\frac{x}{15}\right)=90$$

Multiply 120 and 8 to get 960.

$$\frac{960}{15}x-210\left(\frac{x}{6}+\frac{x}{15}\right)=90$$

Divide 960 by 15 to get 64.

$$64x-210\left(\frac{x}{6}+\frac{x}{15}\right)=90$$

Combine \frac{x}{6} and \frac{x}{15} to get \frac{7}{30}x.

$$64x-210\times \frac{7}{30}x=90$$

Express 210\times \frac{7}{30} as a single fraction.

$$64x-\frac{210\times 7}{30}x=90$$

Multiply 210 and 7 to get 1470.

$$64x-\frac{1470}{30}x=90$$

Divide 1470 by 30 to get 49.

$$64x-49x=90$$

Combine 64x and -49x to get 15x.

$$15x=90$$

Divide both sides by 15.

$$x=\frac{90}{15}$$

Divide 90 by 15 to get 6.

$$x=6$$