Solve 2/3(3/2(x-1)-3)=2x-5

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

Solve for x

$$x=2$$

Steps for Solving Linear Equation

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

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

Multiply \frac{3}{2} and -1 to get -\frac{3}{2}.

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

Convert 3 to fraction \frac{6}{2}.

$$\frac{2}{3}\left(\frac{3}{2}x-\frac{3}{2}-\frac{6}{2}\right)=2x-5$$

Since -\frac{3}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}\left(\frac{3}{2}x+\frac{-3-6}{2}\right)=2x-5$$

Subtract 6 from -3 to get -9.

$$\frac{2}{3}\left(\frac{3}{2}x-\frac{9}{2}\right)=2x-5$$

Use the distributive property to multiply \frac{2}{3} by \frac{3}{2}x-\frac{9}{2}.

$$\frac{2}{3}\times \frac{3}{2}x+\frac{2}{3}\left(-\frac{9}{2}\right)=2x-5$$

Cancel out \frac{2}{3} and its reciprocal \frac{3}{2}.

$$x+\frac{2}{3}\left(-\frac{9}{2}\right)=2x-5$$

Multiply \frac{2}{3} times -\frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$x+\frac{2\left(-9\right)}{3\times 2}=2x-5$$

Cancel out 2 in both numerator and denominator.

$$x+\frac{-9}{3}=2x-5$$

Divide -9 by 3 to get -3.

$$x-3=2x-5$$

Subtract 2x from both sides.

$$x-3-2x=-5$$

Combine x and -2x to get -x.

$$-x-3=-5$$

Add 3 to both sides.

$$-x=-5+3$$

Add -5 and 3 to get -2.

$$-x=-2$$

Multiply both sides by -1.

$$x=2$$