Question 8:
Given that 3<√x−2<4 and x is an integer. List all the possible values of x.Given that 3<√x−2<4 and x is an integer. List all the possible values of x.
Solution:
3<√x−2<432<x−2<429<x−2x>11 or x−2<16x<1811<x<18x=12, 13, 14, 15, 16, 173<√x−2<432<x−2<429<x−2x>11 or x−2<16x<1811<x<18x=12, 13, 14, 15, 16, 17
Given that 3<√x−2<4 and x is an integer. List all the possible values of x.Given that 3<√x−2<4 and x is an integer. List all the possible values of x.
Solution:
3<√x−2<432<x−2<429<x−2x>11 or x−2<16x<1811<x<18x=12, 13, 14, 15, 16, 173<√x−2<432<x−2<429<x−2x>11 or x−2<16x<1811<x<18x=12, 13, 14, 15, 16, 17
Question 9:
Find the biggest and the smallest integer of x that satisfy
3x + 2 ≥ –4 and 4 – x > 0.
Solution:
3x + 2 ≥ –4
3x ≥ –4 – 2
3x ≥ –6
x ≥ –2
4 – x > 0
–x > –4
x < 4
Smallest integer of x is –2, and the biggest integer of x is 3.
Find the biggest and the smallest integer of x that satisfy
3x + 2 ≥ –4 and 4 – x > 0.
Solution:
3x + 2 ≥ –4
3x ≥ –4 – 2
3x ≥ –6
x ≥ –2
4 – x > 0
–x > –4
x < 4
Smallest integer of x is –2, and the biggest integer of x is 3.
Question 10:
If x≤h≤y satisfy the two inequalities 7−h2≤5 and 3(h+2)≤20+h, find the values of x and y.If x≤h≤y satisfy the two inequalities 7−h2≤5 and 3(h+2)≤20+h, find the values of x and y.
Solution:
7−h2≤5−h2≤5−7−h≤−4h≥43(h+2)≤20+h3h+6≤20+h2h≤14h≤74≤h≤7∴x=4,y=7
If x≤h≤y satisfy the two inequalities 7−h2≤5 and 3(h+2)≤20+h, find the values of x and y.If x≤h≤y satisfy the two inequalities 7−h2≤5 and 3(h+2)≤20+h, find the values of x and y.
Solution:
7−h2≤5−h2≤5−7−h≤−4h≥43(h+2)≤20+h3h+6≤20+h2h≤14h≤74≤h≤7∴x=4,y=7