Question

Solve:
\[1\ge 15-7x\ge 2x-27,x\in N\]

Answer 1

Hint: To solve linear inequality in one variable we will simplify it in similar way of linear equation and we will take variable terms to the one side and constants to the other side and then we will simplify it for value of variable(x) but we should keep in mind the notation of inequality which decides the interval of solution.

Complete step by step answer:
According to the question:
Given in equation is:
\[1\ge 15-7x \ge 2x-27\]
So, we have:
\[1\ge 15-7x\text{ and 15-7x} \ge 2x-27\]
\[\Rightarrow 7x\ge 15-1\text{ and }-2x-7x\ge-27-15\]
\[\Rightarrow 7x\ge 14\text{ and }-9x\ge-42\]
\[\Rightarrow x\ge 2\text{ and }-x\ge\dfrac{-42}{9}\]
\[\Rightarrow x\ge 2\text{ and x}\ge\dfrac{14}{3}\]
\[\Rightarrow 2\le x \le \dfrac{14}{3}\]
But as \[x\in N\]
The solution set is \[\{2,3,4\}\]

Note:
Lineаr inequаlities аnd lineаr equаtiоns аre similar kinds of things but the main difference is if we multiply linear inequalities by -1 then the sign of inequality will be changed but in equations it won’t happen. Generally students make mistakes while multiplying the inequality by minus 1 as they forget to change the sign of inequality. And sometimes students forget to check that boundary points are included or excluded.