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ChickenWings
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Please help me understand how to get the solution to the following:
If 7x is a multiple of 210, must x be a multiple of 12?
Thank you!
If 7x is a multiple of 210, must x be a multiple of 12?
Thank you!
MarkFL said:I would begin by finding the prime factorization of 210, which is:
\(\displaystyle 210=2\cdot3\cdot5\cdot7\)
Now, if $7x$ is a multiple of 210, then we may write:
\(\displaystyle 7x=210n=2\cdot3\cdot5\cdot7\cdot n\)
Now dividing through by 7, we find:
\(\displaystyle x=2\cdot3\cdot5\cdot n\)
What can you conclude from this?
The equation for solving 7x=210 is x=30.
The value of x=30 because when you divide 210 by 7, you get 30. This is the only value that satisfies the equation 7x=210.
No, there is no other value of x that can satisfy the equation 7x=210. 30 is the only solution.
X has to be a multiple of 12 because 7 is not a multiple of 12. Therefore, in order for 7x to equal 210, x must be a multiple of 12 in order for the two sides of the equation to be equal.
Think of it this way: 7x=210 means that x has to be multiplied by 7 in order to equal 210. Since 7 is not a factor of 210, x must be a multiple of 7 in order for it to be possible for the equation to be true. And since 12 is a multiple of 7, x must also be a multiple of 12 in order to satisfy the equation.