Solve (a+6)*(a-9)>(a+11)*(a-14)

$$( a + 6 ) \cdot ( a - 9 ) > ( a + 11 ) \cdot ( a - 14 )$$

Solve for a

$$a\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply a+6 by a-9 and combine like terms.

$$a^{2}-3a-54>\left(a+11\right)\left(a-14\right)$$

Use the distributive property to multiply a+11 by a-14 and combine like terms.

$$a^{2}-3a-54>a^{2}-3a-154$$

Subtract a^{2} from both sides.

$$a^{2}-3a-54-a^{2}>-3a-154$$

Combine a^{2} and -a^{2} to get 0.

$$-3a-54>-3a-154$$

Add 3a to both sides.

$$-3a-54+3a>-154$$

Combine -3a and 3a to get 0.

$$-54>-154$$

This is true for any a.

$$a\in \mathrm{R}$$