Question

1)write an inequality

a. the sum of three times a number and 2 lies between 7 and 14

b.seven less than 4 times a number is at most 44 and at least -24.

2)which is not a solution of -4 is less than or equal to 2-6x less than or equal to 8.

3) 2x-1<x+2<6x+12

a. 0
b. 1
c. 2
d.-1

Answer 1

1a. 7 < (3x+2)<14.

2. -4<= 2-6x <= 8.
-4-2 <= -6x <= 8-2
-6 <= -6x <= 6
1 >= X >= -1
-1<= X <= 1.
S0 X can be any value from -1 to positive 1.

C. 2 is False. Not a solution.

3. 2x-1<x+2 < 6x+12
Solve the compound inequality as 2 separate inequalities.

2x-1 < x+2.
2x-x < 2+1
X < 3.

x+2 < 6x+12
x-6x < 12-2
-5x < 12-2
-5x < 10
X > -2.

Solution set: -2 < X < 3.

All values of X between -2 and 3 satisfies the compound inequality and
each single inequality.