Elementary Algebra

Treat it like an equation with the exception that if you multiply or divide by a negative value, the direction of the inequality reverses. You want to isolate x.

What would you say a good first step is?
 
I looked at the purple review math and I am still stuck can you just walk me step by step in order to get the answer?
 
If 20-4/5 x >16, then? I don't know help.
TEMPORARILY turn it into an equation. (This is NOT the fastest way, but it is the least error prone.)

\(\displaystyle 20 - \frac{4}{5}x > 16\ translated\ into\ 20 - \frac{4}{5}x = 16 \implies\)

\(\displaystyle 5\left(20 - \frac{4}{5}x\right) = 5 * 16 \implies 100 - 4x = 80 \implies 100 - 80 = 4x \implies 4x = 20 \implies x = 5.\)

Now pick a convenient number bigger than 5. Because we have to multiply by 4/5, I am going to choose 10, but you can choose any number bigger than 5.

\(\displaystyle 20 - \frac{4}{5} * 10 = 20 - 8 = 12 < 16.\)

So 5 does not work because it leads to a result = 16. And numbers bigger than 5 do not work because they lead to a result < 16.

So the answer must be x < 5.

Now check your answer. Pick a convenient number less than 5. Let's try zero.

\(\displaystyle 20 - \frac{4}{5} * 0 = 20 - 0 = 20 > 16.\) It checks.
 
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