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

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

Solve for x

$$x=-\frac{24}{35}\approx -0.685714286$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Cancel out 2 and 2.

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

Multiply 2 and 2 to get 4.

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

Add 4 and 1 to get 5.

$$\frac{2}{3}x-1=24x+3\times 5$$

Multiply 3 and 5 to get 15.

$$\frac{2}{3}x-1=24x+15$$

Subtract 24x from both sides.

$$\frac{2}{3}x-1-24x=15$$

Combine \frac{2}{3}x and -24x to get -\frac{70}{3}x.

$$-\frac{70}{3}x-1=15$$

Add 1 to both sides.

$$-\frac{70}{3}x=15+1$$

Add 15 and 1 to get 16.

$$-\frac{70}{3}x=16$$

Multiply both sides by -\frac{3}{70}, the reciprocal of -\frac{70}{3}.

$$x=16\left(-\frac{3}{70}\right)$$

Express 16\left(-\frac{3}{70}\right) as a single fraction.

$$x=\frac{16\left(-3\right)}{70}$$

Multiply 16 and -3 to get -48.

$$x=\frac{-48}{70}$$

Reduce the fraction \frac{-48}{70} to lowest terms by extracting and canceling out 2.

$$x=-\frac{24}{35}$$