Solve 4(2x+5)/9+3(2-x)/4=5x-2/2+10-15x/6

$$\frac { 4 ( 2 x + 5 ) } { 9 } + \frac { 3 ( 2 - x ) } { 4 } = \frac { 5 x - 2 } { 2 } + \frac { 10 - 15 x } { 6 }$$

Solve for x

$$x=-22$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 9,4,2,6.

$$4\times 4\left(2x+5\right)+9\times 3\left(2-x\right)=18\left(5x-2\right)+6\left(10-15x\right)$$

Multiply 4 and 4 to get 16.

$$16\left(2x+5\right)+9\times 3\left(2-x\right)=18\left(5x-2\right)+6\left(10-15x\right)$$

Use the distributive property to multiply 16 by 2x+5.

$$32x+80+9\times 3\left(2-x\right)=18\left(5x-2\right)+6\left(10-15x\right)$$

Multiply 9 and 3 to get 27.

$$32x+80+27\left(2-x\right)=18\left(5x-2\right)+6\left(10-15x\right)$$

Use the distributive property to multiply 27 by 2-x.

$$32x+80+54-27x=18\left(5x-2\right)+6\left(10-15x\right)$$

Add 80 and 54 to get 134.

$$32x+134-27x=18\left(5x-2\right)+6\left(10-15x\right)$$

Combine 32x and -27x to get 5x.

$$5x+134=18\left(5x-2\right)+6\left(10-15x\right)$$

Use the distributive property to multiply 18 by 5x-2.

$$5x+134=90x-36+6\left(10-15x\right)$$

Use the distributive property to multiply 6 by 10-15x.

$$5x+134=90x-36+60-90x$$

Add -36 and 60 to get 24.

$$5x+134=90x+24-90x$$

Combine 90x and -90x to get 0.

$$5x+134=24$$

Subtract 134 from both sides.

$$5x=24-134$$

Subtract 134 from 24 to get -110.

$$5x=-110$$

Divide both sides by 5.

$$x=\frac{-110}{5}$$

Divide -110 by 5 to get -22.

$$x=-22$$