Question

Solve the linear inequality $ - 12x \leqslant - 72$ and find the range of x.

Answer 1

Hint: We will know the condition and properties of linear inequality. We will multiply the equation by minus sign to make x sign free. We will divide the equation by 12 to free x from the coefficient and get the range of x.

Complete step by step answer:
We have given below the condition for solving the inequality.
If any number or variable is added or removed on both sides, the inequality remains unchanged. Similarly, multiplying the same integer or variable on both sides has no effect on its value. The inequality sign is flipped or reversed when inequality is divided or multiplied by a negative variable or number on both sides. It is not required to change the direction of inequality when we divide inequality by a positive integer.
We have given $ - 12x \leqslant - 72$
We will multiply the whole equation by -1
We know that the direction of the inequality changes when it is multiplied by negative number,
$12x \geqslant 72$
We have divided the whole equation by 12, we get
$x \geqslant 6$
So, the value of x is equal to and greater than 6.
Hence, the equation $ - 12x \leqslant - 72$ has solution $x \geqslant 6$.

Note:
 We should be careful when the direction of inequity changes. We can also solve these types of questions using the graphical method. Graphical method for solving one variable inequality is done using the number line.