Question

Solve the following equation and choose the correct options from the given choices $-5\left( x+4 \right)>30$; $x\in Z.$
a)$\left\{ 3,4,5,...... \right\}$
b)$\left\{ -9,-8,-7,....... \right\}$
c)$\left\{ -11,-12,-13,......... \right\}$
d)None of These

Answer 1

Hint: We will solve this inequality and then accordingly choose the correct option. We will expand $-5\left( x+4 \right)>30$as $-5x+20$ and then transpose -20 from LHS to RHS and then we will solve this inequality accordingly.

Complete step-by-step answer:
It is given in the question that to solve the question that to solve the inequality $-5\left( x+4 \right)>30$ where x belongs to any integer number. Now, given equation $-5\left( x+4 \right)>30$, on expanding LHS, we get- $-5x-20>30$ . On transposing -20 from LHS to RHS, we get- $-5x>50$. On dividing LHS and RHS with 5, we get- $-x>10$ . Then, on multiplying LHS and RHS with -1, we get- $x<-10$, it is because whenever we multiply with -1 on both sides the inequality sign changes accordingly, thus in our solution also inequality sign changes as $x<-10$.
It means that we have to select an option in which the all the value of x is less than -10, thus we get only c) option in which all the value of x is less than -10 as $-10>-11,-10>-12$ and $-10>-11$ and so on. Therefore, option c) is the correct answer.

Note: Usually students forget to change the sign of inequality after multiplication with -1 on both sides, which results in formation of wrong answers. Thus it is recommended to change inequality according to both sides otherwise we will get exactly the opposite answer from the actual one.