Solve 3(2p+1/3)>4(3p-1/2)

$$3 ( 2 p + \frac { 1 } { 3 } ) > 4 ( 3 p - \frac { 1 } { 2 } )$$

Solve for p

$$p<\frac{1}{2}$$

Solution Steps

Use the distributive property to multiply 3 by 2p+\frac{1}{3}.

$$6p+3\times \frac{1}{3}>4\left(3p-\frac{1}{2}\right)$$

Cancel out 3 and 3.

$$6p+1>4\left(3p-\frac{1}{2}\right)$$

Use the distributive property to multiply 4 by 3p-\frac{1}{2}.

$$6p+1>12p+4\left(-\frac{1}{2}\right)$$

Express 4\left(-\frac{1}{2}\right) as a single fraction.

$$6p+1>12p+\frac{4\left(-1\right)}{2}$$

Multiply 4 and -1 to get -4.

$$6p+1>12p+\frac{-4}{2}$$

Divide -4 by 2 to get -2.

$$6p+1>12p-2$$

Subtract 12p from both sides.

$$6p+1-12p>-2$$

Combine 6p and -12p to get -6p.

$$-6p+1>-2$$

Subtract 1 from both sides.

$$-6p>-2-1$$

Subtract 1 from -2 to get -3.

$$-6p>-3$$

Divide both sides by -6. Since -6 is negative, the inequality direction is changed.

$$p<\frac{-3}{-6}$$

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

$$p<\frac{1}{2}$$