Question

How do you solve \[5x + 2 \leqslant 17\] ?

Answer 1

Hint: In the given question, we are required to solve an algebraic inequality. To solve an algebraic inequality as the one given in the question, we can use algebraic rules and properties such as transposition and algebraic operations like addition, subtraction, multiplication and division. If the same mathematical thing is done on both sides of an algebraic equation or inequality, then it remains unchanged. But by multiplying or dividing an algebraic inequality by a negative real number, the sign of the inequality changes.

Complete step by step solution:
We are given an algebraic inequality \[5x + 2 \leqslant 17\] to solve.
So, \[5x + 2 \leqslant 17\]
Subtracting \[2\] from both sides of the inequality, we get,
 \[ \Rightarrow 5x \leqslant 17 - 2\]
Simplifying further, we get,
 \[ \Rightarrow 5x \leqslant 15\]
Dividing both sides of the inequality by \[5\] , we get,
 \[ \Rightarrow x \leqslant \left( {\dfrac{{15}}{5}} \right)\]
We know that on dividing both sides of an algebraic inequality by a positive number, the sign of inequality remains unchanged. Hence, the sign of inequality does not change.
Simplifying further, we get,
 \[ \Rightarrow x \leqslant 3\]
So, the solution of the given algebraic inequality consists of all real values of variable x that are less than or equal to \[3\] .
So, the correct answer is “ \[ x \leqslant 3\] ”.

Note: Method of transposition involves doing the exact same mathematical thing on both sides of an equation with aim of simplification in mind. This method can be used to solve various algebraic equations and inequalities like the one given in question with ease. The inequality given in the question can also be solved using the graphical method.