Solve 5/4-7/4x=6/x-1/24

$$\frac { 5 } { 4 } - \frac { 7 } { 4 x } = \frac { 6 } { x } - \frac { 1 } { 24 }$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 24x, the least common multiple of 4,4x,x,24.

$$24x\times \frac{5}{4}-6\times 7=24\times 6+24x\left(-\frac{1}{24}\right)$$

Multiply 24 and \frac{5}{4} to get 30.

$$30x-6\times 7=24\times 6+24x\left(-\frac{1}{24}\right)$$

Multiply -6 and 7 to get -42.

$$30x-42=24\times 6+24x\left(-\frac{1}{24}\right)$$

Multiply 24 and 6 to get 144.

$$30x-42=144+24x\left(-\frac{1}{24}\right)$$

Multiply 24 and -\frac{1}{24} to get -1.

$$30x-42=144-x$$

Add x to both sides.

$$30x-42+x=144$$

Combine 30x and x to get 31x.

$$31x-42=144$$

Add 42 to both sides.

$$31x=144+42$$

Add 144 and 42 to get 186.

$$31x=186$$

Divide both sides by 31.

$$x=\frac{186}{31}$$

Divide 186 by 31 to get 6.

$$x=6$$