Question

what is the solution to the absolute value equation |3x - 9| = -7?
there is no solution.

question 4
a weather forecaster determines that there is between a 55 and 65 percent chance of rain in the evening. which equation will produce the values for the minimum and maximum chance of rain in the evening?
|x - 0.6| = 0.05
|x + 0.6| = 0.05
|x + 0.05| = 0.6
|x - 0.05| = 0.6

Explanation:

Question 3

Step1: Recall absolute value property

The absolute value of any real number, denoted as $|A|$, is always non-negative, meaning $|A| \geq 0$ for all real $A$.

Step2: Compare to given equation

The equation is $|3x - 9| = -7$. Since the right-hand side is $-7 < 0$, which contradicts the non-negative property of absolute values, there is no real number $x$ that satisfies the equation.

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Question 4

Step1: Find midpoint of the range

First, calculate the midpoint (average) of 55% (0.55) and 65% (0.65):
$\frac{0.55 + 0.65}{2} = 0.6$

Step2: Find distance from midpoint

Calculate the distance from the midpoint to either end of the range:
$0.65 - 0.6 = 0.05$

Step3: Write absolute value equation

For a value $x$ between $a$ and $b$, the absolute value equation is $|x - \text{midpoint}| = \text{distance}$. Substituting the values gives:
$|x - 0.6| = 0.05$

Answer:

There is no solution.