Solve x*(35/6-21/3)=1

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

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

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

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

Multiply 3 and 6 to get 18.

$$6x\left(\frac{18+5}{6}-\frac{2\times 3+1}{3}\right)=6$$

Add 18 and 5 to get 23.

$$6x\left(\frac{23}{6}-\frac{2\times 3+1}{3}\right)=6$$

Multiply 2 and 3 to get 6.

$$6x\left(\frac{23}{6}-\frac{6+1}{3}\right)=6$$

Add 6 and 1 to get 7.

$$6x\left(\frac{23}{6}-\frac{7}{3}\right)=6$$

Least common multiple of 6 and 3 is 6. Convert \frac{23}{6} and \frac{7}{3} to fractions with denominator 6.

$$6x\left(\frac{23}{6}-\frac{14}{6}\right)=6$$

Since \frac{23}{6} and \frac{14}{6} have the same denominator, subtract them by subtracting their numerators.

$$6x\times \frac{23-14}{6}=6$$

Subtract 14 from 23 to get 9.

$$6x\times \frac{9}{6}=6$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$6x\times \frac{3}{2}=6$$

Express 6\times \frac{3}{2} as a single fraction.

$$\frac{6\times 3}{2}x=6$$

Multiply 6 and 3 to get 18.

$$\frac{18}{2}x=6$$

Divide 18 by 2 to get 9.

$$9x=6$$

Divide both sides by 9.

$$x=\frac{6}{9}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$x=\frac{2}{3}$$