Solve 5p-(41/4+4p)>21/3-1

$$5 p - ( 4 \frac { 1 } { 4 } + 4 p ) > 2 \frac { 1 } { 3 } - 1$$

Solve for p

$$p>\frac{67}{12}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,3. Since 12 is positive, the inequality direction remains the same.

$$60p-12\left(\frac{4\times 4+1}{4}+4p\right)>4\left(2\times 3+1\right)-12$$

Multiply 4 and 4 to get 16.

$$60p-12\left(\frac{16+1}{4}+4p\right)>4\left(2\times 3+1\right)-12$$

Add 16 and 1 to get 17.

$$60p-12\left(\frac{17}{4}+4p\right)>4\left(2\times 3+1\right)-12$$

Use the distributive property to multiply -12 by \frac{17}{4}+4p.

$$60p-12\times \frac{17}{4}-48p>4\left(2\times 3+1\right)-12$$

Express -12\times \frac{17}{4} as a single fraction.

$$60p+\frac{-12\times 17}{4}-48p>4\left(2\times 3+1\right)-12$$

Multiply -12 and 17 to get -204.

$$60p+\frac{-204}{4}-48p>4\left(2\times 3+1\right)-12$$

Divide -204 by 4 to get -51.

$$60p-51-48p>4\left(2\times 3+1\right)-12$$

Combine 60p and -48p to get 12p.

$$12p-51>4\left(2\times 3+1\right)-12$$

Multiply 2 and 3 to get 6.

$$12p-51>4\left(6+1\right)-12$$

Add 6 and 1 to get 7.

$$12p-51>4\times 7-12$$

Multiply 4 and 7 to get 28.

$$12p-51>28-12$$

Subtract 12 from 28 to get 16.

$$12p-51>16$$

Add 51 to both sides.

$$12p>16+51$$

Add 16 and 51 to get 67.

$$12p>67$$

Divide both sides by 12. Since 12 is positive, the inequality direction remains the same.

$$p>\frac{67}{12}$$