4(4k + 2) - 8(k - 1) < 3(2k + 4) - 2 (your statement)

16k + 8 - 8k + 8 < 6k + 12 - 2 (apply distributive property)

8k + 16 < 6k + 10 (collect terms)

8k - 6k + 16 - 16 < 6k - 6k + 10 - 16 (subtract 6k; subtract 16)

2k < -6 (collect terms)

2k/2 < -6/2 (divide by 2)

______

Inequalities are solved likewise to equations, but with one exemption. Multiplication or division by a negative integer reverses the sense of the equality. For instance:

-x

x

Realise that in step 6 of your problem, the sense of the equality was

16k + 8 - 8k + 8 < 6k + 12 - 2 (apply distributive property)

8k + 16 < 6k + 10 (collect terms)

8k - 6k + 16 - 16 < 6k - 6k + 10 - 16 (subtract 6k; subtract 16)

2k < -6 (collect terms)

2k/2 < -6/2 (divide by 2)

**k < -3**(solution)______

Inequalities are solved likewise to equations, but with one exemption. Multiplication or division by a negative integer reverses the sense of the equality. For instance:

-x

**>**2x

**<**-2 (divide by -2 on both sides)Realise that in step 6 of your problem, the sense of the equality was

*not*altered due to the fact that we divided by "+2".