Solve 3x/2+5x+2/3-x+1/2=8x

$$\frac{ 3x }{ 2 } + \frac{ 5x+2 }{ 3 } - \frac{ x+1 }{ 2 } =8x$$

Solve for x

$$x=\frac{1}{32}=0.03125$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\times 3x+2\left(5x+2\right)-3\left(x+1\right)=48x$$

Multiply 3 and 3 to get 9.

$$9x+2\left(5x+2\right)-3\left(x+1\right)=48x$$

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

$$9x+10x+4-3\left(x+1\right)=48x$$

Combine 9x and 10x to get 19x.

$$19x+4-3\left(x+1\right)=48x$$

Use the distributive property to multiply -3 by x+1.

$$19x+4-3x-3=48x$$

Combine 19x and -3x to get 16x.

$$16x+4-3=48x$$

Subtract 3 from 4 to get 1.

$$16x+1=48x$$

Subtract 48x from both sides.

$$16x+1-48x=0$$

Combine 16x and -48x to get -32x.

$$-32x+1=0$$

Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$-32x=-1$$

Divide both sides by -32.

$$x=\frac{-1}{-32}$$

Fraction \frac{-1}{-32} can be simplified to \frac{1}{32} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{1}{32}$$