Answer :
To find the value of [tex]\( x \)[/tex] such that [tex]\( 24x \)[/tex] is a multiple of 3, you need to use the property that the sum of the digits of a number must be a multiple of 3 for the number itself to be a multiple of 3.
Here's a step-by-step explanation:
1. Identify the number:
- The number is [tex]\( 24x \)[/tex], where [tex]\( x \)[/tex] is a single digit.
2. Determine the sum of digits:
- The digits of [tex]\( 24x \)[/tex] are 2, 4, and [tex]\( x \)[/tex].
- Therefore, the sum of these digits is [tex]\( 6 + x \)[/tex] (since [tex]\( 2 + 4 = 6 \)[/tex]).
3. Set the condition for a multiple of 3:
- We want [tex]\( 24x \)[/tex] to be a multiple of 3, so [tex]\( 6 + x \)[/tex] has to be a multiple of 3.
4. Find possible values for [tex]\( 6 + x \)[/tex]:
- Possible values of [tex]\( 6 + x \)[/tex] that are multiples of 3 are: 6, 9, 12, and 15.
5. Solve for [tex]\( x \)[/tex]:
- If [tex]\( 6 + x = 6 \)[/tex], then [tex]\( x = 0 \)[/tex].
- If [tex]\( 6 + x = 9 \)[/tex], then [tex]\( x = 3 \)[/tex].
- If [tex]\( 6 + x = 12 \)[/tex], then [tex]\( x = 6 \)[/tex].
- If [tex]\( 6 + x = 15 \)[/tex], then [tex]\( x = 9 \)[/tex].
6. Identify possible values of [tex]\( x \)[/tex]:
- Therefore, the possible values for [tex]\( x \)[/tex] are 0, 3, 6, and 9.
In conclusion, the digit [tex]\( x \)[/tex] can have four possible values: 0, 3, 6, or 9.
Here's a step-by-step explanation:
1. Identify the number:
- The number is [tex]\( 24x \)[/tex], where [tex]\( x \)[/tex] is a single digit.
2. Determine the sum of digits:
- The digits of [tex]\( 24x \)[/tex] are 2, 4, and [tex]\( x \)[/tex].
- Therefore, the sum of these digits is [tex]\( 6 + x \)[/tex] (since [tex]\( 2 + 4 = 6 \)[/tex]).
3. Set the condition for a multiple of 3:
- We want [tex]\( 24x \)[/tex] to be a multiple of 3, so [tex]\( 6 + x \)[/tex] has to be a multiple of 3.
4. Find possible values for [tex]\( 6 + x \)[/tex]:
- Possible values of [tex]\( 6 + x \)[/tex] that are multiples of 3 are: 6, 9, 12, and 15.
5. Solve for [tex]\( x \)[/tex]:
- If [tex]\( 6 + x = 6 \)[/tex], then [tex]\( x = 0 \)[/tex].
- If [tex]\( 6 + x = 9 \)[/tex], then [tex]\( x = 3 \)[/tex].
- If [tex]\( 6 + x = 12 \)[/tex], then [tex]\( x = 6 \)[/tex].
- If [tex]\( 6 + x = 15 \)[/tex], then [tex]\( x = 9 \)[/tex].
6. Identify possible values of [tex]\( x \)[/tex]:
- Therefore, the possible values for [tex]\( x \)[/tex] are 0, 3, 6, and 9.
In conclusion, the digit [tex]\( x \)[/tex] can have four possible values: 0, 3, 6, or 9.
