Question

I literally just don’t know how to do it

Answer 1

You have a compound inequality,

`\frac{18-x}5 > 3 \lor \frac{x+7}2 < 4`

which is the same as saying

`\frac{18-x}5 > 3 \text{ or } \frac{x+7}2 < 4`

(the
`\lor` symbol means "or") which in plain English translates to

"x belongs to some set of numbers such that the quantity (18 - x)/5 is larger than 3, or the quantity (x + 7)/2 is smaller than 4"

Solve the two inequalities separately. On their own, there are no hidden tricks to solving them.

(18 - x)/5 > 3

Multiply both sides by 5 :

18 - x > 15

Isolate x :

18 - 15 > x

x < 3

(x + 7)/2 < 4

Multiply both sides by 2 :

x + 7 < 8

Isolate x :

x < 8 - 7

x < 1

So the solution to the compound inequality is x < 3 or x < 1, meaning "the set of real numbers x that are either smaller than 3 or smaller than 1". But if x < 1, then x is automatically smaller than 3, so the "or" solution can be condensed into a single inequality, x < 3.

The thing about "or" statements in math is that the compound condition, "(condition 1) or (condition 2)", is met if at least one of condition 1 or condition 2 is met.