Question

Find all real numbers x such that 3x - 4 < 5 and -8x - 19 < 21

Answer 1

the numbers are -5 and 3

Explanation:

First of all, the question is asking you to find the values of x from the given inequalities.

-8x -19<21 and 3x - 4 < 5

group all liked terms, in other words, make x and its coefficient stand alone.

-8x < 21 + 19 and 3x < 5 + 4

-19 became +19 because it crossed the sign <, also -4 became +4 because it crossed the sign <.

so we get

-8x < 40 and 3x < 9

we divide each "x" by its coefficient

`( - 8x)/( - 8) < (40)/( - 8) \: and \: (3x)/(3) < (9)/(3)`

then we get

x < -5 and x < 3

but x is positive so it's greater than -5 so we get

x > -5 and x < 3