Question

How do you solve $3x + 7 > 4x + 2$?

Answer 1

Hint: Here we need to find the solution for the inequality given. So, let us consider the given equation first and then start solving. To get the solution we have gathered all x terms at one side and all other constant terms at another side. To do this we use some mathematical operations such as addition, subtraction, multiplication and try to simplify the given inequality. Make sure that the variable x is at L.H.S. and then find the solution for the problem.

Complete step by step solution:
For solving the question, let us consider the given equation,
$3x + 7 > 4x + 2$ …… (1)
We are asked to find the solution for the above inequality.
For solving the given problem, we have to bring all the terms containing x on one side and constant terms on the other side.
Now subtracting $3x$ on both sides of the equation (1), we get,
$ \Rightarrow 3x + 7 - 3x > 4x + 2 - 3x$
Rearranging the terms we get,
$ \Rightarrow 3x - 3x + 7 > 4x - 3x + 2$
Combining the like terms $3x - 3x = 0$
Combining the like terms $4x - 3x = x$
Hence we have,
$ \Rightarrow 0 + 7 > x + 2$
$ \Rightarrow 7 > x + 2$ …… (2)
By observing the equation (2), we can see that the term x is at R.H.S. which is not good to see. So let us rewrite the equation (2) as,
$ \Rightarrow x + 2 < 7$
Now subtracting by 2 on both the sides we get,
$ \Rightarrow x + 2 - 2 < 7 - 2$
Combining like terms $2 - 2 = 0$
Combining like terms $7 - 2 = 5$
Hence we have,
$ \Rightarrow x + 0 < 5$
$ \Rightarrow x < 5$

Hence we can say that by solving the inequality $3x + 7 > 4x + 2$ we get the solution as, $x < 5$.

Note: Remember that when transferring any variable or number to the other side, the signs of the same will be changed to the opposite sign.
When both sides of the equation are added or subtracted by a positive number the inequality sign remains the same and when both sides of the equation are multiplied or divided by a negative number then the inequality gets reversed.