Question

How do you solve the linear equation \[5x+5=3\left( x-3 \right)\]?

Answer 1

Hint: From the question, it is clear that we have to find the value of n in the equation \[5x+5=3\left( x-3 \right)\]. By simply doing some calculations, this equation can be solved and the value of n can be found.

Complete step-by-step solution:
From the question, we were given to solve \[5x+5=3\left( x-3 \right)\]. So, it is clear that we have to find the value of n in the given equation \[5x+5=3\left( x-3 \right)\].
Let us assume the given equation as equation (1).
\[\Rightarrow 5x+5=3\left( x-3 \right)\]…………..(1)
Now the RHS part opens up the brackets by multiplying \[3\] with \[x\] and \[3\]. We get
Now equation (1) becomes as
\[\Rightarrow 5x+5=3x-9\]……………..(2)
Now add \[9\] on both sides
\[\Rightarrow 5x+5+9=3x-9+9\]……………..(3)
After simplification, we get
\[\Rightarrow 5x+14=3x\]…………….(4)
Now subtract \[14\] from both sides.
\[\Rightarrow 5x+14-14=3x-14\]
After simplification, we get
\[\Rightarrow 5x=3x-14\]……………(5)
Now subtract \[3x\] from both sides.
\[\Rightarrow 5x-3x=3x-14-3x\]
After simplification, we get
\[\Rightarrow 2x=-14\]
Now divide with \[2\] on both sides.
\[\Rightarrow \dfrac{2x}{2}=\dfrac{-14}{2}\]
\[\Rightarrow x=-7\]……………….(6)
Now from equation (6) it is clear that the value of \[x\] is \[-7\].
So, by solving \[5x+5=3\left( x-3 \right)\], we get that the value of \[x\] is equal to \[-7\].

Note: Students may make calculation mistakes while solving this problem. Calculation mistakes should be avoided while solving this problem, if a small mistake is done then the final answer will get interrupted. So, calculation mistakes should be avoided and each and every step should be done in a careful manner to get a correct final answer.