Solve t+3/2+t+4/3=t-1/4+1/6

$$\frac { t + 3 } { 2 } + \frac { t + 4 } { 3 } = \frac { t - 1 } { 4 } + \frac { 1 } { 6 }$$

Solve for t

$$t=-5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 2,3,4,6.

$$6\left(t+3\right)+4\left(t+4\right)=3\left(t-1\right)+2$$

Use the distributive property to multiply 6 by t+3.

$$6t+18+4\left(t+4\right)=3\left(t-1\right)+2$$

Use the distributive property to multiply 4 by t+4.

$$6t+18+4t+16=3\left(t-1\right)+2$$

Combine 6t and 4t to get 10t.

$$10t+18+16=3\left(t-1\right)+2$$

Add 18 and 16 to get 34.

$$10t+34=3\left(t-1\right)+2$$

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

$$10t+34=3t-3+2$$

Add -3 and 2 to get -1.

$$10t+34=3t-1$$

Subtract 3t from both sides.

$$10t+34-3t=-1$$

Combine 10t and -3t to get 7t.

$$7t+34=-1$$

Subtract 34 from both sides.

$$7t=-1-34$$

Subtract 34 from -1 to get -35.

$$7t=-35$$

Divide both sides by 7.

$$t=\frac{-35}{7}$$

Divide -35 by 7 to get -5.

$$t=-5$$