Question

Solve the equation: $\dfrac{1}{{10}} - \dfrac{7}{x} = 35$

Answer 1

Hint:
Solving the equation means finding the unknown value. To find \[x\] we can combine the constant terms to one side. Then cross-multiply and simplify to get the value.

Complete step by step solution:
Consider the given equation
$\dfrac{1}{{10}} - \dfrac{7}{x} = 35$
Rearrange the terms by making constant terms on the same side and variable on the other.
Here the term with variable is $\dfrac{7}{x}$.
So keep it alone on one side and remaining terms on the other side.
So we have,
$\dfrac{1}{{10}} - 35 = \dfrac{7}{x}$
Simplifying left hand side we get,
$\dfrac{{1 - 350}}{{10}} = \dfrac{7}{x}$
$ \Rightarrow - \dfrac{{349}}{{10}} = \dfrac{7}{x}$
Cross-multiplying the above equation we get,
$ - 349x = 7 \times 10$
$ \Rightarrow 349x = 70$
We need to find $x$.
So make $x$ alone in the left hand side.
Dividing both sides of the above equation by $349$ we get,
$x = \dfrac{{70}}{{349}}$

Therefore the solution of the given equation is $x = \dfrac{{70}}{{349}}$

Additional information:
We use different methods to solve equations. For simplification we cancel the common terms if any. Also multiply or divide by a common number on both sides. We can do any of the operations such as addition, multiplication, subtraction or division on both sides of the equation. But the thing is that when dividing we should ensure that it is a non-zero term since division by zero is not defined. We can also multiply the numerator and denominator of a fraction by the same number without changing the value of the fraction.

Note:
This can be solved in another way.
Consider $\dfrac{1}{{10}} - \dfrac{7}{x} = 35$
Cross multiplying the left hand side we get,
$\dfrac{{x - 70}}{{10x}} = 35$
Multiplying both sides by $10x$ we get,
$x - 70 = 35 \times 10x$
$ \Rightarrow x - 70 = 350x$
Rearranging the terms we get,
$x - 350x = 70$
$ \Rightarrow - 349x = 70$
Then we can proceed as earlier.