Solve 276=4(11/2*3/4t+3/4t+t)

$$276 = 4 ( 1 \frac { 1 } { 2 } \times \frac { 3 } { 4 } t + \frac { 3 } { 4 } t + t )$$

Solve for t

$$t=24$$

Steps for Solving Linear Equation

Divide both sides by 4.

$$\frac{276}{4}=\frac{1\times 2+1}{2}\times \frac{3}{4}t+\frac{3}{4}t+t$$

Divide 276 by 4 to get 69.

$$69=\frac{1\times 2+1}{2}\times \frac{3}{4}t+\frac{3}{4}t+t$$

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

$$276=2\left(1\times 2+1\right)\times \frac{3}{4}t+3t+4t$$

Multiply 1 and 2 to get 2.

$$276=2\left(2+1\right)\times \frac{3}{4}t+3t+4t$$

Add 2 and 1 to get 3.

$$276=2\times 3\times \frac{3}{4}t+3t+4t$$

Multiply 2 and 3 to get 6.

$$276=6\times \frac{3}{4}t+3t+4t$$

Express 6\times \frac{3}{4} as a single fraction.

$$276=\frac{6\times 3}{4}t+3t+4t$$

Multiply 6 and 3 to get 18.

$$276=\frac{18}{4}t+3t+4t$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$276=\frac{9}{2}t+3t+4t$$

Combine \frac{9}{2}t and 3t to get \frac{15}{2}t.

$$276=\frac{15}{2}t+4t$$

Combine \frac{15}{2}t and 4t to get \frac{23}{2}t.

$$276=\frac{23}{2}t$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{23}{2}t=276$$

Multiply both sides by \frac{2}{23}, the reciprocal of \frac{23}{2}.

$$t=276\times \frac{2}{23}$$

Express 276\times \frac{2}{23} as a single fraction.

$$t=\frac{276\times 2}{23}$$

Multiply 276 and 2 to get 552.

$$t=\frac{552}{23}$$

Divide 552 by 23 to get 24.

$$t=24$$