Solve 50/6-38-1/3+2a-1/2<1

$$\frac { 50 } { 6 } - \frac { 38 - 1 } { 3 } + \frac { 2 a - 1 } { 2 } < 1$$

Solve for a

$$a<\frac{11}{2}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 6,3,2. Since 6 is positive, the inequality direction remains the same.

$$50-2\left(38-1\right)+3\left(2a-1\right)<6$$

Subtract 1 from 38 to get 37.

$$50-2\times 37+3\left(2a-1\right)<6$$

Multiply -2 and 37 to get -74.

$$50-74+3\left(2a-1\right)<6$$

Subtract 74 from 50 to get -24.

$$-24+3\left(2a-1\right)<6$$

Use the distributive property to multiply 3 by 2a-1.

$$-24+6a-3<6$$

Subtract 3 from -24 to get -27.

$$-27+6a<6$$

Add 27 to both sides.

$$6a<6+27$$

Add 6 and 27 to get 33.

$$6a<33$$

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

$$a<\frac{33}{6}$$

Reduce the fraction \frac{33}{6} to lowest terms by extracting and canceling out 3.

$$a<\frac{11}{2}$$