Solve 3t+1/16-2t-3/7=t+3/8+3t-1/14

$$\frac { 3 t + 1 } { 16 } - \frac { 2 t - 3 } { 7 } = \frac { t + 3 } { 8 } + \frac { 3 t - 1 } { 14 }$$

Solve for t

$$t=\frac{3}{7}\approx 0.428571429$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 112, the least common multiple of 16,7,8,14.

$$7\left(3t+1\right)-16\left(2t-3\right)=14\left(t+3\right)+8\left(3t-1\right)$$

Use the distributive property to multiply 7 by 3t+1.

$$21t+7-16\left(2t-3\right)=14\left(t+3\right)+8\left(3t-1\right)$$

Use the distributive property to multiply -16 by 2t-3.

$$21t+7-32t+48=14\left(t+3\right)+8\left(3t-1\right)$$

Combine 21t and -32t to get -11t.

$$-11t+7+48=14\left(t+3\right)+8\left(3t-1\right)$$

Add 7 and 48 to get 55.

$$-11t+55=14\left(t+3\right)+8\left(3t-1\right)$$

Use the distributive property to multiply 14 by t+3.

$$-11t+55=14t+42+8\left(3t-1\right)$$

Use the distributive property to multiply 8 by 3t-1.

$$-11t+55=14t+42+24t-8$$

Combine 14t and 24t to get 38t.

$$-11t+55=38t+42-8$$

Subtract 8 from 42 to get 34.

$$-11t+55=38t+34$$

Subtract 38t from both sides.

$$-11t+55-38t=34$$

Combine -11t and -38t to get -49t.

$$-49t+55=34$$

Subtract 55 from both sides.

$$-49t=34-55$$

Subtract 55 from 34 to get -21.

$$-49t=-21$$

Divide both sides by -49.

$$t=\frac{-21}{-49}$$

Reduce the fraction \frac{-21}{-49} to lowest terms by extracting and canceling out -7.

$$t=\frac{3}{7}$$