Solve x-1/6=22/5+21/2

$$x - \frac { 1 } { 6 } = 2 \frac { 2 } { 5 } + 2 \frac { 1 } { 2 }$$

Solve for x

$$x = \frac{76}{15} = 5\frac{1}{15} \approx 5.066666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 6,5,2.

$$30x-5=6\left(2\times 5+2\right)+15\left(2\times 2+1\right)$$

Multiply 2 and 5 to get 10.

$$30x-5=6\left(10+2\right)+15\left(2\times 2+1\right)$$

Add 10 and 2 to get 12.

$$30x-5=6\times 12+15\left(2\times 2+1\right)$$

Multiply 6 and 12 to get 72.

$$30x-5=72+15\left(2\times 2+1\right)$$

Multiply 2 and 2 to get 4.

$$30x-5=72+15\left(4+1\right)$$

Add 4 and 1 to get 5.

$$30x-5=72+15\times 5$$

Multiply 15 and 5 to get 75.

$$30x-5=72+75$$

Add 72 and 75 to get 147.

$$30x-5=147$$

Add 5 to both sides.

$$30x=147+5$$

Add 147 and 5 to get 152.

$$30x=152$$

Divide both sides by 30.

$$x=\frac{152}{30}$$

Reduce the fraction \frac{152}{30} to lowest terms by extracting and canceling out 2.

$$x=\frac{76}{15}$$