Question

How do you solve the equation $2x+3x-4x>9$ ?

Answer 1

Hint: In the given equation we have all the variables on one side and the constant on the other side. Hence we will proceed to simplify the equation. Now we can add and subtract the terms with the same power and variable. Hence we will simplify the equation and find the condition on x. Now we will use the condition to find the solution set for the equation.

Complete step by step solution:
Now we are given with a linear inequality in x.
To solve the inequality we will first separate all the variable terms and the constants.
Since we already have all the variable terms on LHS and the constant on RHS we can easily simplify the equation.
Now we know that we can add the terms with the same variable and power.
Hence we get 2x + 3x = 5x
Hence can write the given equation as $5x-4x>9$
Now again subtracting the terms on LHS we get,
$x>9$
Hence we have the solution of the given equation is $x>9$ .
Now this means for all values which are greater than 9 the equation holds.
Hence we have the solution of the equation is $\left( 9,\infty \right)$ .

Note: Now note that while solving inequality we add and subtract the terms without changing the inequality but when we multiply or divide a term to the equation then first we have to check the sign of the term. If it is positive then there is no change in inequality but if the term is negative then we reverse the inequality.