Five times a number is divided by 7 more than that number. If the result is 0 then what was the original number?
Five times a number is divided by 7 more than that number. If the result is 0 then what was the original number?
5n
––––– = 0
n + 7
The only way this can happen is n = zero.
.
+135 When five times a number is divided by 7 more than the number and the result is 2, then the number is 14/3, which is solved using the linear equation in one variable 5x/(x+ 7) = 2, where x is the required number.
What are linear equations in one variable?
Linear equations are first-order equations. Lines in the coordinate system are determined by linear equations. A linear equation in one variable is defined as an equation with a homogeneous variable of degree 1 (i.e. only one variable).
How to solve the given question?
In the question, we are asked to find a number, which satisfies the statement, "Five times a number is divided by 7 more than the number. The result of this division is 2".
We assume the number to be x.
Now we try to form a linear equation in one variable from the given statement.
Five times a number is 5x.
7 more than a number is x + 7.
We are said that five times a number is divided by 7 more than a number. This can be shown as 5x/(x + 7).
Now, the result is given as 2, which can be shown as:
5x/(x+ 7) = 2, which is the required linear equation in one variable.
To get the number, we solve the equation using the following steps:
5x/(x+ 7) = 2
or, {5x/(x+ 7)}*(x + 7) = 2*(x + 7) (Multiplying both sides by (x + 7))
or, 5x = 2x + 14 (Simplifying)
or, 5x - 2x = 2x + 14 - 2x (Subtracting 2x from both sides)
or, 3x = 14 (Simplifying)
or, 3x/3 = 14/3 (Dividing both sides by 3)
or, x = 14/3 (Simplifying)
∴ When five times a number is divided by 7 more than the number and the result is 2, then the number is 14/3, which is solved using the linear equation in one variable 5x/(x+ 7) = 2, where x is the required number.
