Solve 3/2left(2left(x-1/2right)+2/3right)=5x

$$\frac{ 3 }{ 2 } \left( 2 \left( x- \frac{ 1 }{ 2 } \right) + \frac{ 2 }{ 3 } \right) =5x$$

Solve for x

$$x=-\frac{1}{4}=-0.25$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by x-\frac{1}{2}.

$$\frac{3}{2}\left(2x+2\left(-\frac{1}{2}\right)+\frac{2}{3}\right)=5x$$

Cancel out 2 and 2.

$$\frac{3}{2}\left(2x-1+\frac{2}{3}\right)=5x$$

Convert -1 to fraction -\frac{3}{3}.

$$\frac{3}{2}\left(2x-\frac{3}{3}+\frac{2}{3}\right)=5x$$

Since -\frac{3}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{3}{2}\left(2x+\frac{-3+2}{3}\right)=5x$$

Add -3 and 2 to get -1.

$$\frac{3}{2}\left(2x-\frac{1}{3}\right)=5x$$

Use the distributive property to multiply \frac{3}{2} by 2x-\frac{1}{3}.

$$\frac{3}{2}\times 2x+\frac{3}{2}\left(-\frac{1}{3}\right)=5x$$

Cancel out 2 and 2.

$$3x+\frac{3}{2}\left(-\frac{1}{3}\right)=5x$$

Multiply \frac{3}{2} times -\frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$3x+\frac{3\left(-1\right)}{2\times 3}=5x$$

Cancel out 3 in both numerator and denominator.

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

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

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

Subtract 5x from both sides.

$$3x-\frac{1}{2}-5x=0$$

Combine 3x and -5x to get -2x.

$$-2x-\frac{1}{2}=0$$

Add \frac{1}{2} to both sides. Anything plus zero gives itself.

$$-2x=\frac{1}{2}$$

Divide both sides by -2.

$$x=\frac{\frac{1}{2}}{-2}$$

Express \frac{\frac{1}{2}}{-2} as a single fraction.

$$x=\frac{1}{2\left(-2\right)}$$

Multiply 2 and -2 to get -4.

$$x=\frac{1}{-4}$$

Fraction \frac{1}{-4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$x=-\frac{1}{4}$$