Solve 18x+5/5+6x-5/15-2x-3/6=54x-7/9

$$\frac { 18 x + 5 } { 5 } + \frac { 6 x - 5 } { 15 } - \frac { 2 x - 3 } { 6 } = \frac { 54 x - 7 } { 9 }$$

Solve for x

$$x=\frac{5}{6}\approx 0.833333333$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 90, the least common multiple of 5,15,6,9.

$$18\left(18x+5\right)+6\left(6x-5\right)-15\left(2x-3\right)=10\left(54x-7\right)$$

Use the distributive property to multiply 18 by 18x+5.

$$324x+90+6\left(6x-5\right)-15\left(2x-3\right)=10\left(54x-7\right)$$

Use the distributive property to multiply 6 by 6x-5.

$$324x+90+36x-30-15\left(2x-3\right)=10\left(54x-7\right)$$

Combine 324x and 36x to get 360x.

$$360x+90-30-15\left(2x-3\right)=10\left(54x-7\right)$$

Subtract 30 from 90 to get 60.

$$360x+60-15\left(2x-3\right)=10\left(54x-7\right)$$

Use the distributive property to multiply -15 by 2x-3.

$$360x+60-30x+45=10\left(54x-7\right)$$

Combine 360x and -30x to get 330x.

$$330x+60+45=10\left(54x-7\right)$$

Add 60 and 45 to get 105.

$$330x+105=10\left(54x-7\right)$$

Use the distributive property to multiply 10 by 54x-7.

$$330x+105=540x-70$$

Subtract 540x from both sides.

$$330x+105-540x=-70$$

Combine 330x and -540x to get -210x.

$$-210x+105=-70$$

Subtract 105 from both sides.

$$-210x=-70-105$$

Subtract 105 from -70 to get -175.

$$-210x=-175$$

Divide both sides by -210.

$$x=\frac{-175}{-210}$$

Reduce the fraction \frac{-175}{-210} to lowest terms by extracting and canceling out -35.

$$x=\frac{5}{6}$$