Answer:
1. -6 ≤ x < -1, conjunction
2. x > 10 or x ≤ 6, disjunction
3. 7 ≤ x ≤ 12, conjunction
4. x ≥ -3 or x < -9, disjunction
Step-by-step explanation:
These inequalities are called "compound inequalities." Each compound inequality is made up of two simple inequalities.
A compound inequality of the type 5 < x < 8 means x > 5 and x < 8. Since the word between the simple inequalities is "and", it is a conjunction.
A compound inequality of the type "x < 3 or x > 12" uses the word "or" between the simple inequalities. It is called a disjunction.
1.
-4 ≤ x + 2 < 1
Conjunction
For this type of inequality, do what you need to do to get x alone in the middle section. Do the same to all three "sides" of the inequality.
The middle section has x + 2. We want x alone,s o w must subtract 2. We subtract 2 from all three sides.
-4 - 2 ≤ x + 2 - 2 < 1 - 2
-6 ≤ x < -1
2. 5x - 4 > 46 or 4x ≤ 3x + 6
Disjunction
In this type of compound inequality, solve each inequality by itself, and always keep the word "or" between the inequalities.
5x - 4 > 46 or 4x ≤ 3x + 6
5x - 4 + 4 > 46 + 4 or 4x - 3x ≤ 3x - 3x + 6
5x > 50 or x ≤ 6
x > 10 or x ≤ 6
3. Similar to problem 1.
Conjunction
10 ≤ 2x - 4 ≤ 20
Add 4 to all sections.
14 ≤ 2x ≤ 24
Divide all sections by 2.
7 ≤ x ≤ 12
4.
6 - 2x ≤ 12 or 7 + 2x < -11
Disjunction
-2x ≤ 6 or 2x < -18
x ≥ -3 or x < -9
