Solve and Graph.
1 answer:
The value of x from the inequality equation | 4x + 1 | ≤ 6 , is
-7/4 ≤ x ≤ 5/4
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the equation be A
The value of the equation A is | 4x + 1 | ≤ 6 be equation (1)
From the modulus function rule , we know
If , | x | ≤ a , then -a ≤ x ≤ a
So , on simplifying the equation , we get
-6 ≤ 4x + 1 ≤ 6
Now , the two values are
4x + 1 ≥ -6 be equation (2)
4x + 1 ≤ 6 be equation (3)
From equation (2) , 4x + 1 ≥ -6
Subtracting 1 on both sides , we get
4x ≥ -7
Divide by 4 , we get
x ≥ -7/4
And , From equation (3) , 4x + 1 ≤ 6
Subtracting 1 on both sides , we get
4x ≤ 5
Divide by 4 on both sides , we get
x ≤ 5/4
Therefore , the solution is -7/4 ≤ x ≤ 5/4 and the graph is given below
Hence , The value of x from the inequality equation | 4x + 1 | ≤ 6 , is
-7/4 ≤ x ≤ 5/4
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The two temperatures could be removed so that the average of the remaining numbers is the same as the average of the original set of numbers are -1 and -9
Step-by-step explanation:
The formula of the average of a set of data is , where
- S is the sum of the data in the set
- N is the number of the data in the set
∵ The low temperatures in Anchorage, Alaska, for a week were
− 6, − 3, − 1, 1, − 3, − 9, and − 14 degrees Celsius
∴ The set of the data is { -6 , -3 , -1 , 1 , -3 , -9 , -14}
- Add the data in the set
∵ S = -6 + -3 + -1 + 1 + -3 + -9 + -14
∴ S = -35
∵ The set has 7 data
∴ N = 7
- Use the formula of the average above to find it
∴
∴ A = -5
∴ The average of the original set of numbers is -5
To keep the average the same after removing two numbers multiply the average by the new number of data to find the new sum
∵ The number of data after removing two numbers is 5
∴ N = 5
∵ A = -5
- By using the rule of average
∴
- Multiply both sides by 5
∴ -25 = S
∴ The new sum is -25
- Lets find which two numbers of have a sum of -10 because
the difference between -35 and -25 is -10
∵ -1 + -9 = -10
∵ -6 + -3 + 1 + -3 + -14 = -25
∴ We could removed -1 and -9
The two temperatures could be removed so that the average of the remaining numbers is the same as the average of the original set of numbers are -1 and -9
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You can learn more about the average in brainly.com/question/10764770
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