Question

How do you solve for x in $ 4x + 3 < 5x $ ?

Answer 1

Hint: The value of x in $ 4x + 3 < 5x $ can be found by using the method of transposition. Method of transposition involves doing the exact same mathematical thing on both sides of an equation or an inequality with aim of simplification in mind. This method can be used to solve various algebraic inequalities like the one given in question with ease.

Complete step-by-step answer:
We would use the method of transposition to find the value of x in $ 4x + 3 < 5x $ . Method of transposition involves doing the exact same thing on both sides of an equation with the aim of bringing like terms together and isolating the variable or the unknown term in order to simplify the equation and finding value of the required parameter.
Now, In order to find the value of x, we need to isolate x from the rest of the parameters.
So, $ 4x + 3 < 5x $
Taking all the terms consisting x to right side of the equation by subtracting the $ 4x $ term from both sides of the equation, we get,
 $ \Rightarrow $ \[4x + 3 - 4x < 5x - 4x\]
Cancelling the like terms with opposite sign, we get,
 $ \Rightarrow $ $ 3 < 5x - 4x $
Simplifying the calculations, we get,
 $ \Rightarrow 3 < x $
So, we get the solution of the inequality $ 4x + 3 < 5x $ as $ x > 3 $ . So, all the real values of x greater than $ 3 $ are the solution of the given algebraic inequality and satisfy the inequality.

Note: The given problem deals with algebraic inequality. There is no fixed way of solving a given algebraic inequality. Algebraic inequality can be solved in various ways. The sign of inequality remains the same if we multiply or divide both sides of the inequality by a positive number but the sign of inequality reverses when we multiply or divide both sides of the inequality by a negative number.