a l g e b r a o n e.

Question

5x-7x+9>x+3(2x-6)

why is the direction of the inequality symbol reversed in the equation above ?

Answer 1

Just switch everything around:

See watch.....

1 > 0 is the same as 0 < 1

They are both true statements....

In general, if A > B then B < A

So write it like this:

x + 3(2x - 6) < 5x - 7x + 9

x +6x - 18 < 5x - 7x + 9 <--- distributive

7x - 18 < -2x + 9 <--- combines like terms on both sides

7x - 18 + 2x < 9 <--- adds 2x to both sides

9x - 18 < 9 <-- combines like terms again

9x < 9 + 18 <--- adds 18 to both sides

9x < 27 <--- combines like terms

x < 3 <-- divides both sides by 9