Solve t+7/3=1-3t+17/6

$$\frac { t + 7 } { 3 } = 1 - \frac { 3 t + 17 } { 6 }$$

Solve for t

$$t=-5$$

Steps for Solving Linear Equation

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

$$2\left(t+7\right)=6-\left(3t+17\right)$$

Use the distributive property to multiply 2 by t+7.

$$2t+14=6-\left(3t+17\right)$$

To find the opposite of 3t+17, find the opposite of each term.

$$2t+14=6-3t-17$$

Subtract 17 from 6 to get -11.

$$2t+14=-11-3t$$

Add 3t to both sides.

$$2t+14+3t=-11$$

Combine 2t and 3t to get 5t.

$$5t+14=-11$$

Subtract 14 from both sides.

$$5t=-11-14$$

Subtract 14 from -11 to get -25.

$$5t=-25$$

Divide both sides by 5.

$$t=\frac{-25}{5}$$

Divide -25 by 5 to get -5.

$$t=-5$$