Answer:
- 14 ≤ 6x + 4 < 16 ⇔ First (Top) Number Line
- 4x + 3 > - 9 and -6x ≤ 12 ⇔ Third (Bottom) Number Line
- 4x + 3 > - 9 and -6x ≤ 12 ⇔ Second (Middle) Number Line
Step-by-step explanation:
Solve each inequality so that only x appears as the left or right side of the inequality which makes it easier to represent on the number line
Inequality: -14 ≤ 6x + 4 < 16
Subtract 4 from left and right sides:
-14 - 4 ≤ 6x < 16 - 4
=> -18 ≤ 6x < 12
Divide by 6:
-3 ≤ x < 2
This will be represented on the number line by a filled circle at -3 and a hollow circle at 2
This corresponds to the first number line
Inequality -4x + 3 > - 9 and -6x ≤ 12
-4x + 3 > - 9 can be transformed as follows
Multiply by -1 (this will change direction of inequality):
4x - 3 < 9
Add 3
4x < 12
Divide by 4:
x < 3
-6x ≤ 12
=> 6x ≥ -12 (multiply by -1)
=> x ≥ -2 (divide by 6)
So the compound inequality is
x ≥ - 2 and x < 3
=> -2 ≤ x < 3
Corresponds to filled circle at -2 and hollow circle at 3 with the segment between -2 and 3 since it is and
This is number line 3
Inequality -4x + 3 > - 9 or -6x ≤ 12
The end values are the same -2(filled) on the left and 3(hollow) on the . The only change is in the segments representing the range of values since it is an or condition
Therefore the segments would be one pointing from -2 to the left and the other pointing from 3 to the right
Number line 3
