Solve 14a/3-1+12-a/4=(2a-5)*1/2

$$1 \frac { 4 a } { 3 } - 1 + \frac { 12 - a } { 4 } = ( 2 a - 5 ) \cdot \frac { 1 } { 2 }$$

Solve for a

$$a=-54$$

Steps for Solving Linear Equation

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

$$4\times 4a-12+3\left(12-a\right)=12\left(2a-5\right)\times \frac{1}{2}$$

Multiply 4 and 4 to get 16.

$$16a-12+3\left(12-a\right)=12\left(2a-5\right)\times \frac{1}{2}$$

Use the distributive property to multiply 3 by 12-a.

$$16a-12+36-3a=12\left(2a-5\right)\times \frac{1}{2}$$

Add -12 and 36 to get 24.

$$16a+24-3a=12\left(2a-5\right)\times \frac{1}{2}$$

Combine 16a and -3a to get 13a.

$$13a+24=12\left(2a-5\right)\times \frac{1}{2}$$

Multiply 12 and \frac{1}{2} to get \frac{12}{2}.

$$13a+24=\frac{12}{2}\left(2a-5\right)$$

Divide 12 by 2 to get 6.

$$13a+24=6\left(2a-5\right)$$

Use the distributive property to multiply 6 by 2a-5.

$$13a+24=12a-30$$

Subtract 12a from both sides.

$$13a+24-12a=-30$$

Combine 13a and -12a to get a.

$$a+24=-30$$

Subtract 24 from both sides.

$$a=-30-24$$

Subtract 24 from -30 to get -54.

$$a=-54$$