How do you solve and write the following in interval notation: 3x+4≥5x-8?

2 Answers
Jun 22, 2016

x in (-oo,6]

Explanation:

Remember you can add/subtract the same amount and multiply/divide by any amount greater than zero to both sides of an inequality without invalidating the inequality.

3x+4 >= 5x-8
color(white)("XXX")3x+12 >= 5x

color(white)("XXX")12 >= 2x

color(white)("XXX")6 >= x

or (reversing so x is on the left, which is more common)
color(white)("XXX")x <= 6

Jun 22, 2016

You may add or subtract on both sides of the inequality.

Explanation:

Add 8 to both sides:
3x+4+8>=5x-cancel8+cancel8->3x+12>=5x#

Subtract 3x from both sides:
cancel(3x)-cancel(3x)+12>=5x-3x->12>=2x->

Divide by 2, a positive number:
6>=x->x<=6

->x in [6,oo), where [ means 'inclusive'.

Note: you may be used to a different notation, but I think the above is clear enough to translate.