Respuesta :
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
Answer:
1. -6≤x<-1
conjunction
2.x>10 or x≤6
Disjunction
3.7≤x≤12
Conjunction
4.x ≥-6 or x < -6
Disjunction
5.2≤x≤5
Conjunction
6. x ≤ 54 or x≥66
Disjunction
7. 39< x≤43
Conjunction
Step-by-step explanation:
conjunction is "and" like a sandwich between 2 points
disjunction is " or" like boat oars with a gap for the boat in the middle
1. -4≤x+2<1
Subtract 2 from all sides
-4-2≤x+2-2<1 -2
-6≤x<-1
conjunction
2. 5x-4>46" or " 4x≤3x+6
Add 4 to each side Subtract 3x from each side
5x-4+4 > 46+4 4x-3x≤3x-3x+6
5x >50 x≤6
Divide by 5
5x/5 >50/5
x>10 or x≤6
Disjunction
3. 10≤2x-4≤20
Add 4 to all sides
10≤2x-4≤20
10+4 ≤2x-4+4≤20+4
14≤2x≤24
Divide by 2 on all sides
14/2≤2x/2≤24/2
7≤x≤12
Conjunction
4. 6-2x≤12" or " 7+2x<-11
Subtract 6 from each side Subtract 7 from each side
6-6-2x≤12 or " 7-7+2x<-11-7
-2x≤12 2x<-18
Divide by -2 Divide by 2
Flips the inequality
-2x/-2≥12/-2 2x/2 <-18/2
x ≥-6 or x < -6
Disjunction
5. 5≤2x+1≤11
Subtract 1 from all sides
5-1≤2x+1-1≤11-1
4≤2x≤10
Divide all sides by 2
4/2≤2x/2≤10/2
2≤x≤5
Conjunction
6. 2/3 x-20≤16" or " x/3+10≥32
Add 20 from each side Subtract 10 from each side
2/3 x-20+20 ≤16+20 x/3 +10-10 ≥32 -10
2/3 x ≤36 x/3≥22
Multiply by 3/2 on each side Multiply by 3 on each side
3/2 * 2/3x ≤ 36*3/2 x/3*3 ≥22 *3
x ≤ 54 or x≥66
Disjunction
7. 10<1/4 (x+1)≤11
Multiply all sides by 4
4*10<1/4*4 (x+1)≤11*4
40< (x+1)≤44
Subtract 1 from all sides
40-1< (x+1-1)≤44-1
39< x≤43
Conjunction
