B. –2 < x < 2
C. –6 < x < 2
D. –21 < x < 3
The solution to the inequality |3x + 6| < 12 is -6 < x < 2, which corresponds to option C.
To solve the inequality |3x + 6| < 12, we can break it down into two separate inequalities:
3x + 6 < 12
-(3x + 6) < 12
Solving the first inequality:
3x + 6 < 12
Subtracting 6 from both sides:
3x < 6
Dividing both sides by 3 (since 3 is positive, we don't need to change the direction of the inequality):
x < 2
Solving the second inequality:
-(3x + 6) < 12
Distributing the negative sign:
-3x - 6 < 12
Adding 6 to both sides:
-3x < 18
Dividing both sides by -3 (since -3 is negative, we need to change the direction of the inequality):
x > -6
Combining the solutions from both inequalities, we have:
-6 < x < 2
Therefore, the correct option is C. -6 < x < 2.
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-1/2 + (3/4X4/9)=
Answer:
Step-by-step explanation:
In order to find the answer to this question you must use order of operations and add after finding the common denominator.
P goes first
Solve:
Reduce:
Hope this helps.
Answer:
The correct answer would be negative 1 over 6 also written as -1/6
Step-by-step explanation:
HAVE A GOOD DAY!
The subject of this question is Mathematics at a High School level. The length of the room is twice the width.
The subject of this question is Mathematics and it is at a High School level.
Let the width of the room be represented by w.
Then, the length of the room would be 2 times the width, so it can be represented as 2w.
Since we know that the length is twice the width, we can write the equation:
2w = l
To find the length, we substitute the value of the width into the equation:
2w = 2 * w
l = 2w
So, the length of the room is twice the width.
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0.2
1/2
2%
Step-by-step explanation:
In this case we need to arrange the given number in a order starting with the smallest.
First number is 0.2
Second number is 1/2
Third number is 2%
Firstly, we need to convert these number in same form i.e. decimal form.
1/2 can be written as 0.5
2% can be written as
Now, it is required to arrange these number from smallest to largest. So,
0.02 is the smallest number and 0.5 is the largest number.
Order is : 0.02, 0.2, 0.5
If f(x) = (x + 7)^2, which of the following is g(x) based on the translation?
g(x) = (x + 5^)2
g(x) = (x − 5)^2
g(x) = (x − 9)^2
g(x) = (x + 9)^2
Answer:
The equation for g(x) is:
g(x)=(x+5)^2
Step-by-step explanation:
We are given the information about the graph of the function f(x) and g(x) as:
graph of function f of x open upward and has its vertex at (-7,0).
Graph of function g of x opens upward and has its vertex at (-5,0).
If f(x) = (x + 7)^2; which is a parabola with vertex at (-7,0).
Also as g(x) is formed by the translation of the function f(x) so it will also be a quadratic function such that it's vertex is (-5,0).
so, the equation of g(x) will be:
g(x)=(x+5)^2.
Hence, the translation is a shift of the function f(x) 2 units to the right.