Solve x/5+1/3=x/2*1/4+frac{x}{2}*frac{1}{6}

$$\frac { x } { 5 } + \frac { 1 } { 3 } = \frac { x } { 2 } \times \frac { 1 } { 4 } + \frac { x } { 2 } \times \frac { 1 } { 6 }$$

Solve for x

$$x=40$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 5,3,2,4,6.

$$12x+20=30x\times \frac{1}{4}+30x\times \frac{1}{6}$$

Multiply 30 and \frac{1}{4} to get \frac{30}{4}.

$$12x+20=\frac{30}{4}x+30x\times \frac{1}{6}$$

Reduce the fraction \frac{30}{4} to lowest terms by extracting and canceling out 2.

$$12x+20=\frac{15}{2}x+30x\times \frac{1}{6}$$

Multiply 30 and \frac{1}{6} to get \frac{30}{6}.

$$12x+20=\frac{15}{2}x+\frac{30}{6}x$$

Divide 30 by 6 to get 5.

$$12x+20=\frac{15}{2}x+5x$$

Combine \frac{15}{2}x and 5x to get \frac{25}{2}x.

$$12x+20=\frac{25}{2}x$$

Subtract \frac{25}{2}x from both sides.

$$12x+20-\frac{25}{2}x=0$$

Combine 12x and -\frac{25}{2}x to get -\frac{1}{2}x.

$$-\frac{1}{2}x+20=0$$

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{1}{2}x=-20$$

Multiply both sides by -2, the reciprocal of -\frac{1}{2}.

$$x=-20\left(-2\right)$$

Multiply -20 and -2 to get 40.

$$x=40$$