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# How do you solve $3x+1=5x-10$?

Last updated date: 20th Jun 2024
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Hint: From the question given, we have been asked to solve $3x+1=5x-10$. We can solve the given equation from the question by using some simple transformations. First, we will shift the constants to the LHS and then the terms with the variable x to the RHS. We will then get the equation simplified and then we can solve it easily.

Complete step-by-step solution:
From the question given, we have been given that,
$3x+1=5x-10$
As we have already discussed earlier, we have to make some simple transformations to the above equation to get it simplified.
Shift $10$ from the right hand side of the equation to the left hand side of the equation. By shifting $10$ from right hand side of the equation to the left hand side of the equation, we get
$\Rightarrow 3x+1+10=5x$
Now, simplify the above equation further. By simplifying the above equation further, we get
$\Rightarrow 3x+11=5x$
Now, shift 3x from the left hand side of the equation to the right hand side of the equation. By shifting 3x from left hand side of the equation to the right hand side of the equation, we get
$\Rightarrow 11=5x-3x$
In the right hand side of the above equation, we can clearly see that there is a variable common in both the terms.
So, we know that if the variable is common in the terms, we can simply subtract the constants.
By doing this, we get
$\Rightarrow 11=2x$
Shift $2$ from the right hand side of the equation to the left hand side of the equation. By shifting $2$ from right hand side of the equation to the left hand side of the equation, we get
$\Rightarrow x=\dfrac{11}{2}$
Therefore, the given equation is solved.

Note: Students should be well aware of the transformations that have to be made to the given question to get the given question simplified very easily. Also, students should be very careful while applying the transformation to the given equation for example in transforming the equation by sending LHS to RHS in this case $\Rightarrow 3x+1+10=5x$ $\Rightarrow 11=5x-3x$ this is correct we should not take it as $\Rightarrow 11=5x+3x$ it will give us wrong answer and also be very careful while doing the calculation part.