3) the ideal width of a safety belt strap for a certain automobile is 5 cm. an actual width can vary by at most 0.35 cm. write an absolute value inequality for the range of acceptable widths.
a. |w+5|≤ 0.35
b. |w-0.35| ≤ 5
c. |w+0.35|≤ 5
d. |w-5|≤0.35
my answer is C
4) what number makes this inequality equivalent
-6v ; v>-0.5
To find the absolute value inequality for the range of acceptable widths, we need to consider the given information that the ideal width is 5 cm and the actual width can vary by at most 0.35 cm.
Let's consider the difference between the actual width (w) and the ideal width:
Actual width - Ideal width = w - 5
Since the actual width can vary by at most 0.35 cm, we want to ensure that the difference between the actual width and the ideal width is within this range. In other words, the absolute value of the difference should be less than or equal to 0.35.
Therefore, the correct absolute value inequality for the range of acceptable widths is:
|w - 5| ≤ 0.35
Now let's move on to the second question.
To make the inequality -6v equivalent to v > -0.5, we need to find the value that satisfies both expressions.
We can solve the inequality v > -0.5 by adding 0.5 to both sides:
v + 0.5 > -0.5 + 0.5
v + 0.5 > 0
To make both expressions equivalent, we multiply them by -6, which will also reverse the inequality sign:
-6(v + 0.5) < -6(0)
-6v - 3 < 0
This results in the inequality -6v - 3 < 0. So the number that makes the inequality equivalent is -3.
Therefore, the correct answer is -3 for question 4.