Solve 2/3(1/3x-1/2)=4x+21/2

$$\frac{ 2 }{ 3 } ( \frac{ 1 }{ 3 } x- \frac{ 1 }{ 2 } )=4x+2 \frac{ 1 }{ 2 }$$

Solve for x

$$x=-\frac{3}{4}=-0.75$$

Steps for Solving Linear Equation

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

$$4\left(\frac{1}{3}x-\frac{1}{2}\right)=24x+3\left(2\times 2+1\right)$$

Use the distributive property to multiply 4 by \frac{1}{3}x-\frac{1}{2}.

$$4\times \frac{1}{3}x+4\left(-\frac{1}{2}\right)=24x+3\left(2\times 2+1\right)$$

Multiply 4 and \frac{1}{3} to get \frac{4}{3}.

$$\frac{4}{3}x+4\left(-\frac{1}{2}\right)=24x+3\left(2\times 2+1\right)$$

Express 4\left(-\frac{1}{2}\right) as a single fraction.

$$\frac{4}{3}x+\frac{4\left(-1\right)}{2}=24x+3\left(2\times 2+1\right)$$

Multiply 4 and -1 to get -4.

$$\frac{4}{3}x+\frac{-4}{2}=24x+3\left(2\times 2+1\right)$$

Divide -4 by 2 to get -2.

$$\frac{4}{3}x-2=24x+3\left(2\times 2+1\right)$$

Multiply 2 and 2 to get 4.

$$\frac{4}{3}x-2=24x+3\left(4+1\right)$$

Add 4 and 1 to get 5.

$$\frac{4}{3}x-2=24x+3\times 5$$

Multiply 3 and 5 to get 15.

$$\frac{4}{3}x-2=24x+15$$

Subtract 24x from both sides.

$$\frac{4}{3}x-2-24x=15$$

Combine \frac{4}{3}x and -24x to get -\frac{68}{3}x.

$$-\frac{68}{3}x-2=15$$

Add 2 to both sides.

$$-\frac{68}{3}x=15+2$$

Add 15 and 2 to get 17.

$$-\frac{68}{3}x=17$$

Multiply both sides by -\frac{3}{68}, the reciprocal of -\frac{68}{3}.

$$x=17\left(-\frac{3}{68}\right)$$

Express 17\left(-\frac{3}{68}\right) as a single fraction.

$$x=\frac{17\left(-3\right)}{68}$$

Multiply 17 and -3 to get -51.

$$x=\frac{-51}{68}$$

Reduce the fraction \frac{-51}{68} to lowest terms by extracting and canceling out 17.

$$x=-\frac{3}{4}$$