Question

Solve the following inequality (AWARDING MEDAL!)

Answer 1

\[-2 (3x - 8) < 5 (4 - x)\]

Answer 2

Distribute -2 into the parenthesis, can you do that?

Answer 3

\(-2(3x - 8)\)

We have to distribute -2 into the parenthesis, meaning we multiply it to all terms inside the parenthesis.

-2 * 3x

-2 * -8

Can you multiply those?

Answer 4

Yes

Answer 5

Okay, tell me what you get.

Answer 6

i got -6 and -16

Answer 7

Yes, but for the first one we keep the 'x', so we have -6x..and you multiplied the 2nd one incorrectly, it should be positive 16.

So distributing gives us:

\(-6x + 16 < 5(4 - x)\)

Now we have to distribute 5 into the parenthesis.

Multiply:

5 * 4

5 * -x

Answer 8

Tell me what you get.

Answer 9

20 - 5?

Answer 10

Remember, we keep the 'x' so it's 20 - 5x

So we have:

\(-6x + 16 < 20 - 5x\)

Now we add 5x to both sides, what's -6x + 5x?

Answer 11

\[−2(3x−8)<5(4−x)\]
Lets distribute the parenthesis first (The brackets)
\[-6x+16<20-5x\]
Move the \(-5x\) to the RHS, it now becomes positive
\[-6x+16+5x<20-5x+5x\]\[-6x+16+5x<20\cancel{-5x}\cancel{+5x}\]\[-6x+16+5x<20\]\[-x+16<20\]
Do the same for \(16\)
\[-x+16<20\]\[-x+16-16<20-16\]\[-x\cancel{+16}\cancel{-16}<20-16\]\[-x<20-16\]\[-x=4\]
Move the \(-\) from the \(x\). Note, doing this flips the sign from \(<\) to \(>\)
\[-x<4\]\[\frac{-x}{-1}>\frac{4}{-1}\]\[\frac{\cancel{-}x}{\cancel{-1}}>\frac{4}{-1}\]\[x>\frac{4}{-1}\]\[x>-4\]

Answer 12

-1x ?

Answer 13

Yes, so we have:

\(-x + 16 < 20\)

Now subtract 16 to both sides, what's 20 - 16?

Answer 14

Exactly. But we don't normally write the one, so its just \(-x\)

Answer 15

4

Answer 16

Yes, so we have:

\(-x < 4\)

Now we divide -1 to both sides, what's 4 / -1?

Answer 17

-4

Answer 18

Yes, and we flip the sign because we divided by a negative number, so our final answer is:

\(x > -4\)