Question

How do you solve `12x – 5x < 6(x + 7)`?

Answer 1

`x < 42`

Explanation:

`"simplify left side and distribute parenthesis"`

`rArr7x<6x+42larrcolor(blue)"subtract 6x from both sides"`

`rArrx<42" is the solution"`

`x in(-oo,42)larrcolor(blue)"in interval notation"`

Answer 2

You get `x<42`

Explanation:

I would simplify the left side, since `12-5x = 7x`.

Therefore `7x<6(x+7)`
Now `6(x+7)` is the same as multiplying each term in the parenthesis with the number outside, i.e.
`6(x+7) = 6x + 6*7 = 6x+42`
Therefore we have
`7x<6x+42`

So 7 of something should be smaller than 6 of something pluss 42.

I hope it then is easy to see that this is fulfilled if 1 of that something is smaller than 42,
i.e.
`x<42`

Normally we would do it this way, deducting the same amount from each side:
`7x-6x < 6x+42-6x`
Which would give
`x<42`