a) The variable in the inequality is <u>x.</u>
b) The inequality symbol needed <u>< ( or >)</u>
c) The constant is <u>8.</u>
d) The inequality is <u>f(x)<8x .</u>
Step-by-step explanation:
Given,
The person can make less than $8 per hour
To find the correct inequality for this situation.
Let us take,
The person works for x hours.
If the total income of the person for x hours is f(x)
Then, the inequality will be
f(x)<8x
x
-9; x
6 or in interval notation [-9,6]
To find out what are the steps in solving the below inequality:
Given equation is 2x - 3 > 15
The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.
−15≤2x-3≤15
First, subtract 3 from each segment of the system of equations to isolate the x term while keeping the system balanced:
−15−3≤2x-3−3≤15−3
−18≤2x-6≤12
−18≤2x-6≤12
Now, divide each segment of the system by 2 to solve for x while keeping the system balanced:

-9
x
6
or
x
-9; x
6
or in interval notation [-9,6]
on the horizontal axis.
The lines will be a solid line because the inequality operators contain "or equal to" clauses.
We will shade between the lines to show the interval:
Hence the steps to solve an inequality has been show
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Answer:
A. The y-intercept of g(x) is less than the y-intercept of f(x).
Step-by-step explanation:
The x-intercept, or when x = 0, of f(x) is -4, the x-intercept of g(x) is -8, so g(x) are neither greater nor equal to f(x), this marks out C and D. The y-intercept, or when y = 0, is in this case f(x) or g(x). The y-intercept of f(x) is 16, the y-intercept of g(x) is 4, so the y-intercept of g(x) is not equal to the y-intercept of f(x), this marks out B. Now to check A, 4 < 16, so y-intercept of g(x) < y-intercept of f(x), the answer is A