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1. If 42x5 is a multiple of 9 and x is a digit, then find the value of x.

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To determine the value of xx such that 42x542x5 is a multiple of 9, we can sum the digits of the number and see if the result is a multiple of 9. The number 42x542x5 can be written as 420+10x+5420+10x+5. Now, let's consider the sum of the digits: 4+2+0+1+0+x+5=12+x4+2+0+1+0+x+5=12+x For the entire...
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To determine the value of xx such that 42x542x5 is a multiple of 9, we can sum the digits of the number and see if the result is a multiple of 9.

The number 42x542x5 can be written as 420+10x+5420+10x+5.

Now, let's consider the sum of the digits:

4+2+0+1+0+x+5=12+x4+2+0+1+0+x+5=12+x

For the entire number to be divisible by 9, the sum 12+x12+x must be a multiple of 9.

To find the value of xx, we need to find a digit such that 12+x12+x is divisible by 9.

Let's try different values of xx from 0 to 9:

  • If x=0x=0, then 12+0=1212+0=12 which is not divisible by 9.
  • If x=1x=1, then 12+1=1312+1=13 which is not divisible by 9.
  • If x=2x=2, then 12+2=1412+2=14 which is not divisible by 9.
  • If x=3x=3, then 12+3=1512+3=15 which is divisible by 9.

So, x=3x=3 is the value that makes 42x542x5 a multiple of 9.

 
 
 
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