Solve 1/x-7+1/4=1/3

$$\frac { 1 } { x - 7 } + \frac { 1 } { 4 } = \frac { 1 } { 3 }$$

Solve for x

$$x=19$$

Steps for Solving Linear Equation

Variable x cannot be equal to 7 since division by zero is not defined. Multiply both sides of the equation by 12\left(x-7\right), the least common multiple of x-7,4,3.

$$12+12\left(x-7\right)\times \frac{1}{4}=4\left(x-7\right)$$

Multiply 12 and \frac{1}{4} to get 3.

$$12+3\left(x-7\right)=4\left(x-7\right)$$

Use the distributive property to multiply 3 by x-7.

$$12+3x-21=4\left(x-7\right)$$

Subtract 21 from 12 to get -9.

$$-9+3x=4\left(x-7\right)$$

Use the distributive property to multiply 4 by x-7.

$$-9+3x=4x-28$$

Subtract 4x from both sides.

$$-9+3x-4x=-28$$

Combine 3x and -4x to get -x.

$$-9-x=-28$$

Add 9 to both sides.

$$-x=-28+9$$

Add -28 and 9 to get -19.

$$-x=-19$$

Multiply both sides by -1.

$$x=19$$