Solve (21/2:1/2x+5/12)-15/6=frac{2}{3}

$$( 2 \frac { 1 } { 2 } : \frac { 1 } { 2 } x + \frac { 5 } { 12 } ) - 1 \frac { 5 } { 6 } = \frac { 2 } { 3 }$$

Solve for x

$$x=\frac{5}{12}\approx 0.416666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 12,6,3.

$$12\times \frac{\frac{2\times 2+1}{2}}{\frac{1}{2}}x+5-2\left(6+5\right)=8$$

Multiply 2 and 2 to get 4.

$$12\times \frac{\frac{4+1}{2}}{\frac{1}{2}}x+5-2\left(6+5\right)=8$$

Add 4 and 1 to get 5.

$$12\times \frac{\frac{5}{2}}{\frac{1}{2}}x+5-2\left(6+5\right)=8$$

Divide \frac{5}{2} by \frac{1}{2} by multiplying \frac{5}{2} by the reciprocal of \frac{1}{2}.

$$12\times \frac{5}{2}\times 2x+5-2\left(6+5\right)=8$$

Cancel out 2 and 2.

$$12\times 5x+5-2\left(6+5\right)=8$$

Multiply 12 and 5 to get 60.

$$60x+5-2\left(6+5\right)=8$$

Add 6 and 5 to get 11.

$$60x+5-2\times 11=8$$

Multiply -2 and 11 to get -22.

$$60x+5-22=8$$

Subtract 22 from 5 to get -17.

$$60x-17=8$$

Add 17 to both sides.

$$60x=8+17$$

Add 8 and 17 to get 25.

$$60x=25$$

Divide both sides by 60.

$$x=\frac{25}{60}$$

Reduce the fraction \frac{25}{60} to lowest terms by extracting and canceling out 5.

$$x=\frac{5}{12}$$