Solve 6*(1/4+8x/3)=15-18x-15/2+18x

$$6 \cdot ( \frac { 1 } { 4 } + \frac { 8 x } { 3 } ) = 15 - \frac { 18 x - 15 } { 2 } + 18 x$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,3,2.

$$72\left(\frac{1}{4}+\frac{8x}{3}\right)=180-6\left(18x-15\right)+216x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 3 is 12. Multiply \frac{1}{4} times \frac{3}{3}. Multiply \frac{8x}{3} times \frac{4}{4}.

$$72\left(\frac{3}{12}+\frac{4\times 8x}{12}\right)=180-6\left(18x-15\right)+216x$$

Since \frac{3}{12} and \frac{4\times 8x}{12} have the same denominator, add them by adding their numerators.

$$72\times \frac{3+4\times 8x}{12}=180-6\left(18x-15\right)+216x$$

Do the multiplications in 3+4\times 8x.

$$72\times \frac{3+32x}{12}=180-6\left(18x-15\right)+216x$$

Cancel out 12, the greatest common factor in 72 and 12.

$$6\left(3+32x\right)=180-6\left(18x-15\right)+216x$$

Use the distributive property to multiply 6 by 3+32x.

$$18+192x=180-6\left(18x-15\right)+216x$$

Use the distributive property to multiply -6 by 18x-15.

$$18+192x=180-108x+90+216x$$

Add 180 and 90 to get 270.

$$18+192x=270-108x+216x$$

Combine -108x and 216x to get 108x.

$$18+192x=270+108x$$

Subtract 108x from both sides.

$$18+192x-108x=270$$

Combine 192x and -108x to get 84x.

$$18+84x=270$$

Subtract 18 from both sides.

$$84x=270-18$$

Subtract 18 from 270 to get 252.

$$84x=252$$

Divide both sides by 84.

$$x=\frac{252}{84}$$

Divide 252 by 84 to get 3.

$$x=3$$