0>= (5-x)/2 >=-10 — step-by-step solution

1) We have the following 2 conditions:

[1]:

0 \geq \frac{5 - x}{2}

[2]:

\frac{5 - x}{2} \geq -10

2) Let's solve for x:

0 \geq \frac{5 - x}{2}

[1]

⇥The expression

5 - x

is zero at:

⇥

x = 5

⇥Its coefficient of

x

-1

, being negative, it is positive before and negative after

5

Solution obtained [1]:

x \geq 5

3) Let's solve for x:

\frac{5 - x}{2} \geq -10

[2] where

x \geq 5

\frac{5 - x}{2} \geq -10

5 - x \geq -10 \cdot 2

ⓘ A single minus sign does not cancel out, the product of a negative number by a positive number is negative:

-10 \cdot 2

-20

5 - x \geq -20

ⓘ We gather the terms in

x

on the right and the other terms on the left

5 + 20 \geq x

ⓘ Start from

5

and move forward

20

on the number line:

5 + 20

25

25 \geq x

Solution found [2]:

x \leq 25

Intersecting

x \geq 5

and

x \leq 25

gives

x \in [5, 25]

▶Solution:

x \in [5, 25]