Solve 2/1(2x+1/3)=21/6-(x/2-frac{5}{33})

$$\frac { 2 } { 1 } ( 2 x + \frac { 1 } { 3 } ) = 2 \frac { 1 } { 6 } - ( \frac { x } { 2 } - \frac { 5 } { 33 } )$$

Solve for x

$$x=\frac{109}{297}\approx 0.367003367$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 66, the least common multiple of 3,6,2,33.

$$132\left(2x+\frac{1}{3}\right)=11\left(2\times 6+1\right)-66\left(\frac{x}{2}-\frac{5}{33}\right)$$

Use the distributive property to multiply 132 by 2x+\frac{1}{3}.

$$264x+132\times \frac{1}{3}=11\left(2\times 6+1\right)-66\left(\frac{x}{2}-\frac{5}{33}\right)$$

Multiply 132 and \frac{1}{3} to get \frac{132}{3}.

$$264x+\frac{132}{3}=11\left(2\times 6+1\right)-66\left(\frac{x}{2}-\frac{5}{33}\right)$$

Divide 132 by 3 to get 44.

$$264x+44=11\left(2\times 6+1\right)-66\left(\frac{x}{2}-\frac{5}{33}\right)$$

Multiply 2 and 6 to get 12.

$$264x+44=11\left(12+1\right)-66\left(\frac{x}{2}-\frac{5}{33}\right)$$

Add 12 and 1 to get 13.

$$264x+44=11\times 13-66\left(\frac{x}{2}-\frac{5}{33}\right)$$

Multiply 11 and 13 to get 143.

$$264x+44=143-66\left(\frac{x}{2}-\frac{5}{33}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 33 is 66. Multiply \frac{x}{2} times \frac{33}{33}. Multiply \frac{5}{33} times \frac{2}{2}.

$$264x+44=143-66\left(\frac{33x}{66}-\frac{5\times 2}{66}\right)$$

Since \frac{33x}{66} and \frac{5\times 2}{66} have the same denominator, subtract them by subtracting their numerators.

$$264x+44=143-66\times \frac{33x-5\times 2}{66}$$

Do the multiplications in 33x-5\times 2.

$$264x+44=143-66\times \frac{33x-10}{66}$$

Express 66\times \frac{33x-10}{66} as a single fraction.

$$264x+44=143-\frac{66\left(33x-10\right)}{66}$$

Cancel out 66 and 66.

$$264x+44=143-\left(33x-10\right)$$

To find the opposite of 33x-10, find the opposite of each term.

$$264x+44=143-33x-\left(-10\right)$$

The opposite of -10 is 10.

$$264x+44=143-33x+10$$

Add 143 and 10 to get 153.

$$264x+44=153-33x$$

Add 33x to both sides.

$$264x+44+33x=153$$

Combine 264x and 33x to get 297x.

$$297x+44=153$$

Subtract 44 from both sides.

$$297x=153-44$$

Subtract 44 from 153 to get 109.

$$297x=109$$

Divide both sides by 297.

$$x=\frac{109}{297}$$