Question

Solve:
\[3x + \dfrac{2}{3} = 2x + 1\]

Answer 1

Hint:
Here we are given a linear equation in one variable to solve and calculate the value for the \[x\]. Here the equation can be solved easily by collecting the constant terms together and solving and collecting the terms in \[x\] and further solving till the end for getting the precise solution that we want. Let us look at the complete step by step solution for this to see how it is done.

Complete step by step solution:
Here in the question we are asked to solve an equation which is linear and in the one variable that is \[3x + \dfrac{2}{3} = 2x + 1\]
So a linear equation is an equation whose variable maximum power present is \[1\] only solving such equations is the most simplest one if done with concentration and full presence of mind.
For solving such kind of equations we just need to first convert all the fractions if present any in the equation in the simpler form by multiplying the whole equation by the denominator of the fraction or by a common multiple of the denominator if more than one fraction is present In the equation .Then just collecting the like terms together and solving them that is collecting constant terms and further solving them similarly goes for the variable containing terms that is collecting and solving them further and simplifying the answer for the best precision
In the given equation that is \[3x + \dfrac{2}{3} = 2x + 1\]
Firstly simplifying the fraction by multiplying by 3 on both sides we get-
\[9x + 2 = 6x + 3\]
Now collecting the like terms together and solving them we get –
\[9x - 6x = 3 - 2\]
\[3x = 1\]
\[x = \dfrac{1}{3}\]

So, the required answer is \[x = \dfrac{1}{3}\]

Note:
We saw how to solve the linear equation in one variable that is by eliminating the fraction by multiplication and collecting the like terms and solving them further for getting the answer while doing these kind of questions one should keep in mind to copy the terms of the equation from the question correctly and solving them with utter consciousness because the general mistake that a person does in these kind of questions is copying wrong terms and solving them which leads them to the wrong answer ultimately.