Solve z-21/3=51/6

$$z - 2 \frac { 1 } { 3 } = 5 \frac { 1 } { 6 }$$

Solve for z

$$z = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

Steps for Solving Linear Equation

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

$$6z-2\left(2\times 3+1\right)=5\times 6+1$$

Multiply 2 and 3 to get 6.

$$6z-2\left(6+1\right)=5\times 6+1$$

Add 6 and 1 to get 7.

$$6z-2\times 7=5\times 6+1$$

Multiply -2 and 7 to get -14.

$$6z-14=5\times 6+1$$

Multiply 5 and 6 to get 30.

$$6z-14=30+1$$

Add 30 and 1 to get 31.

$$6z-14=31$$

Add 14 to both sides.

$$6z=31+14$$

Add 31 and 14 to get 45.

$$6z=45$$

Divide both sides by 6.

$$z=\frac{45}{6}$$

Reduce the fraction \frac{45}{6} to lowest terms by extracting and canceling out 3.

$$z=\frac{15}{2}$$