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
5) give one solution to the inequality
12x-3x+11<4x-(17-9x).
#3. D
Consider. |w-5| is the difference between w and 5, in either direction. That difference must be at most 0.35
#4. not sure what is intended, unless it's -6v < 3
#5.
The way the question is phrased makes me think there's supposed to be a quadratic.
3) The correct answer is D. To represent the acceptable range of widths, we consider that the actual width can vary by at most 0.35 cm from the ideal width of 5 cm. This can be expressed as:
|w - 5| ≤ 0.35
4) To make the inequality v > -0.5 equivalent to -6v, we need to find a number that is less than -0.5 when multiplied by -6.
Let's solve for v:
v > -0.5
-6v > -0.5 * -6
-6v > 3
So, the number that makes this inequality equivalent is 3.
5) To find one solution to the inequality 12x - 3x + 11 < 4x - (17 - 9x), we can simplify the inequality first.
Simplifying both sides:
9x + 11 < 4x - 17 + 9x
9x + 11 < 13x - 17
Subtracting 9x from both sides:
11 < 4x - 17
Adding 17 to both sides:
11 + 17 < 4x
28 < 4x
Dividing both sides by 4:
7 < x
So, one solution to the inequality is x > 7.
To solve the first problem, you need to consider the stated ideal width of the safety belt strap, which is 5 cm. The actual width is allowed to vary by at most 0.35 cm. To write an absolute value inequality for the range of acceptable widths, you need to determine the difference between the actual width (represented by "w") and the ideal width. Since the actual width can vary by at most 0.35 cm, the absolute value of the difference should be less than or equal to 0.35. Therefore, the correct answer is:
c. |w + 0.35| ≤ 5
Moving on to the second problem, you are given the inequality -6v and you need to find a number that makes it equivalent to v > -0.5. To make these expressions equivalent, you can set them equal to each other and solve for v.
-6v = -0.5
Dividing both sides by -6, you get:
v = (-0.5) / (-6)
v = 0.08333
Therefore, the number that makes the inequality equivalent is 0.08333.
For the third problem, you are asked to provide one solution to the inequality 12x - 3x + 11 < 4x - (17 - 9x). To find a solution, you need to simplify the equation and solve for x.
Starting with the inequality:
12x - 3x + 11 < 4x - (17 - 9x)
Combining like terms:
9x + 11 < 4x - 17 + 9x
-5x + 11 < -17 + 9x
Bringing like terms to one side:
-5x - 9x < -17 - 11
-14x < -28
Dividing both sides by -14 (and reversing the sign due to dividing by a negative number):
x > (-28) / (-14)
x > 2
Therefore, one solution to the inequality is x > 2.