Question

How do you solve \[10+2f=-10-f-10\]?

Answer 1

Hint: We have the expression to solve in terms of \[f\]. We will start by subtracting 10 from both sides of the equality. We have positive 10 in the LHS, so 10 gets cancelled and in the RHS, 10 gets added up. Then, we will add \[f\] on both sides of the equality and calculate. We now have separated the \[f\]terms and the constants and have the equation in terms of \[f\]. Hence, we get the value of \[f\].

Complete step by step solution:
According to the given question, we have to solve in terms of \[f\] for the given expression.
We will use arithmetic operations to get the expression in a simplified form.
We have,
\[10+2f=-10-f-10\]------(1)
We will subtract 10 from both sides of the equality and we get the expression as,
\[\Rightarrow (10+2f)-10=(-10-f-10)-10\]
Solving the obtained expression, we get,
\[\Rightarrow 2f=-10-f-10-10\]
So, in the LHS we had 10 which got cancelled and now in the RHS, we have three -10 which gets added up. We get the expression as,
\[\Rightarrow 2f=-f-30\]
Now, we will add \[f\] on both sides of the equality in the above expression and we have,
\[\Rightarrow 2f+f=-f-30+f\]
Calculating the obtained expression, we get,
\[\Rightarrow 3f=-30\]
We have written the expression in terms of \[f\] and on further solving, we get the value of \[f\] as:
\[\Rightarrow f=-10\]

Therefore, the value of \[f=-10\].

Note: We carried out the calculation by adding and subtracting certain term on both the sides of the equality because when the same entity is added or subtracted from an equality, the equality remains unchanged.
For example – If \[a=b\], then if we add 2 on both the sides, the equality will still remain intact, that is,
\[a+2=b+2\].