Question

How do you solve \[3x+7>4x+9\]?

Answer 1

Hint: For the given we are given to solve the inequality equation \[3x+7>4x+9\]. So let us consider the given equation first and then start solving. To get a solution we have to gather all x terms at one side and all other constants at another side make sure that x is at LHS, and then solve the problem for solution.

Complete step-by-step solution:
For solving this question let us consider the given equation as equation (1).
Let us consider the given equation as equation (1).
\[3x+7>4x+9..................\left( 1 \right)\]
For solving the given problem we have to bring x term in one side and constant term in another side.
Now by subtracting with 3x on both sides of equation (1), we get
\[\Rightarrow 3x+7-3x>4x+9-3x\]
By simplifying a bit to the above equation, we get
\[\Rightarrow 7>x+9\]
Let us consider the above equation as equation (2).
\[\Rightarrow 7>x+9.......................\left( 2 \right)\]
By observing equation (2) we can understand that x term is at RHS which is not good to see. So let us rewrite the equation (2) by changing the sides, we get
\[\Rightarrow x+9<7\]
Let us consider the above equation as equation (3).
\[\Rightarrow x+9<7.........................\left( 3 \right)\]
Now for gathering all constant terms at a side we have to subtract by -9 on both sides.
By subtracting with -9 on both sides of equation (3), we get
\[\Rightarrow x+9-9<7-9\]
By simplifying the above equation a bit, we get
\[\Rightarrow x<-2\]
Let us consider the above equation as equation (4), we get
\[\Rightarrow x<-2...............\left( 4 \right)\]
Hence we can say that by solving the equation (1) i.e. \[3x+7>4x+9\] we get \[x<-2\] .

Note: 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 sign is changed.