Respuesta :
ANSWER
[tex]a = 1,2,3,6[/tex]
EXPLANATION
The given equation is
[tex]ax = 6[/tex]
Divide both sides by [tex]a[/tex]
[tex]
\Rightarrow \: \frac{ax}{a} = \frac{6}{a} [/tex]
Cancel out common factors on the left hand side,
[tex]
\Rightarrow \: x = \frac{6}{a} [/tex]
For this solution to be a whole number, then[tex]a[/tex] should be a factor of
[tex]6[/tex].
The reason is that, factors of 6 will divide exactly in to 6 without a remainder, making the answer a whole number.
The whole numbers that are factors of 6 are,
[tex]1,2,3 \: and \: 6[/tex]
Note that, the set of whole numbers are,
{[tex]0,1,2,3,4,...[/tex]}
[tex]a = 1,2,3,6[/tex]
EXPLANATION
The given equation is
[tex]ax = 6[/tex]
Divide both sides by [tex]a[/tex]
[tex]
\Rightarrow \: \frac{ax}{a} = \frac{6}{a} [/tex]
Cancel out common factors on the left hand side,
[tex]
\Rightarrow \: x = \frac{6}{a} [/tex]
For this solution to be a whole number, then[tex]a[/tex] should be a factor of
[tex]6[/tex].
The reason is that, factors of 6 will divide exactly in to 6 without a remainder, making the answer a whole number.
The whole numbers that are factors of 6 are,
[tex]1,2,3 \: and \: 6[/tex]
Note that, the set of whole numbers are,
{[tex]0,1,2,3,4,...[/tex]}
The whole number values of [tex]a[/tex] are [tex]\boxed{{\mathbf{1,2,3 and 6}}}[/tex] that satisfies the given equation [tex]ax = 6[/tex].
Further explanation:
The whole numbers are the numbers that is easily countable and successors can be defined and it starts from 0.
The set of whole number can be expressed as,
[tex]0,1,2,3,4,5 \ldots[/tex]
The set of whole number is the subset of the set of real numbers.
Given:
The given equation is [tex]ax = 6[/tex].
Step by step explanation:
Step 1:
Divide the given equation [tex]ax = 6[/tex].
[tex]\dfrac{{ax}}{a} = \dfrac{6}{a}[/tex]
Step 2:
Now cancel out the common factors from the left side of the equation.
[tex]x = \dfrac{6}{a}[/tex]
It can be seen that the number [tex]a[/tex] is divisible by 6.
Step 3:
The factor of 6 will divide exactly without leaving any remainder to obtain the whole number.
Now find the whole numbers that is divisible by 6 to obtain the value of [tex]a[/tex].
[tex]1,2,3{\text{ and }}6[/tex]
Therefore, the whole number values of [tex]a[/tex] are [tex]1,2,3{\text{ and }}6[/tex] that satisfies the given equation [tex]ax = 6[/tex].
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Linear equation
Keywords: Whole number, solution, equation, divide, common number, factors, divisible, remainder, set, divide, multiply, fraction, left hand side, common
