Solve 5q/8-21/3=31/6

$$\frac { 5 q } { 8 } - 2 \frac { 1 } { 3 } = 3 \frac { 1 } { 6 }$$

Solve for q

$$q = \frac{44}{5} = 8\frac{4}{5} = 8.8$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 8,3,6.

$$3\times 5q-8\left(2\times 3+1\right)=4\left(3\times 6+1\right)$$

Multiply 3 and 5 to get 15.

$$15q-8\left(2\times 3+1\right)=4\left(3\times 6+1\right)$$

Multiply 2 and 3 to get 6.

$$15q-8\left(6+1\right)=4\left(3\times 6+1\right)$$

Add 6 and 1 to get 7.

$$15q-8\times 7=4\left(3\times 6+1\right)$$

Multiply -8 and 7 to get -56.

$$15q-56=4\left(3\times 6+1\right)$$

Multiply 3 and 6 to get 18.

$$15q-56=4\left(18+1\right)$$

Add 18 and 1 to get 19.

$$15q-56=4\times 19$$

Multiply 4 and 19 to get 76.

$$15q-56=76$$

Add 56 to both sides.

$$15q=76+56$$

Add 76 and 56 to get 132.

$$15q=132$$

Divide both sides by 15.

$$q=\frac{132}{15}$$

Reduce the fraction \frac{132}{15} to lowest terms by extracting and canceling out 3.

$$q=\frac{44}{5}$$