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)
k < -3 (solution)
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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 > 2
x < -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".
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 > 2
x < -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".
