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Scilla [17]
2 years ago
7

Which of the x values are solutions to the inequality 4(2 – x) > –2x – 3(4x + 1)? Check all that apply.

Mathematics
2 answers:
HACTEHA [7]2 years ago
7 0

Answer:

x=0  and  x=10


Step-by-step explanation:

The inequality is given as:  4(2-x)>-2x-3(4x+1)

Using distributive property<em> [ a(b+c)=ab+ac ] </em>and a little algebra, we have:

4(2-x)>-2x-3(4x+1)\\8-4x>-2x-12x-3\\

<em>Taking all the x's to one side and number to another:</em>

-4x+2x+12x>-3-8\\10x>-11\\x>\frac{-11}{10}\\x>-1.1

<em>Now, of the 5 numbers shown, which of them are </em><em>GREATER THAN</em><em> -1.1 ?</em>

They are 0 and 10.

steposvetlana [31]2 years ago
4 0
4(2 - x) > -2x - 3(4x + 1)
8 - 4x > -2x - 12x - 3
-4x + 2x + 12x > -3 - 8
10x > -11
x > -11/10
x > -1.1

Therefore, x = 0 and x = 10 zre solutions to the inequality.
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2 years ago
The greatest common divisor of two positive integers less than $100$ is equal to $3$. Their least common multiple is twelve time
tangare [24]

Answer:

129

Step-by-step explanation:

Let a and b be two numbers.

We have been given that the greatest common divisor of two positive integers less than 100 is equal to 3. We can represent this information as GCD(a,b)=3.

Their least common multiple is twelve times one of the integers. We can represent this information as LCM(a,b)=12a.

Now, we will use property GCD(x,y)*LCM(x,y)=xy.

Upon substituting our given values, we will get:

3*12a=ab

36a=ab

Switch sides:

ab=36a

\frac{ab}{a}=\frac{36a}{a}

b=36

Now, we need to find a number less than 100, which is co-prime with 12 after dividing by 3.

The greatest multiple of 3 less than 100 is 99, but it is not co-prime with 12 after dividing by 3.

Similarly 96 is also not co-prime with 12 after dividing by 3.

We know that greatest multiple of 3 (less than 100), which is co-prime with 12, is 93.

Let us add 36 and 93 to find the largest possible sum of the required two integers as:

36+93=129

Therefore, the required largest possible sum of the two integers is 129.

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2 years ago
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