Answer:
To graph the solution to the inequality |2w + 8| < 12 on the number line, we need to consider two cases:
Case 1: 2w + 8 < 12
In this case, we solve for w by subtracting 8 from both sides of the inequality:
2w + 8 - 8 < 12 - 8
2w < 4
Dividing both sides by 2, we get:
w < 2
Case 2: -(2w + 8) < 12
In this case, we solve for w by multiplying both sides of the inequality by -1 and flipping the inequality sign:
2w + 8 > -12
2w > -12 - 8
2w > -20
Dividing both sides by 2, we get:
w > -10
Now we can plot the solutions on the number line:
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
x x
The solution to the inequality |2w + 8| < 12 is represented by the shaded area between -10 and 2, excluding the endpoints. This means that w can be any value greater than -10 and less than 2, but it cannot be -10 or 2. The "x" marks on the number line indicate the excluded endpoints.
Explanation:
To graph the solution to the inequality |2w + 8| < 12 on the number line, we need to consider two cases:
Case 1: 2w + 8 < 12
In this case, we solve for w by subtracting 8 from both sides of the inequality:
2w + 8 - 8 < 12 - 8
2w < 4
Dividing both sides by 2, we get:
w < 2
Case 2: -(2w + 8) < 12
In this case, we solve for w by multiplying both sides of the inequality by -1 and flipping the inequality sign:
2w + 8 > -12
2w > -12 - 8
2w > -20
Dividing both sides by 2, we get:
w > -10
Now we can plot the solutions on the number line:
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
x x