Question

How do you solve the inequality $3x\ge 15$ ?

Answer 1

When we solve the inequality $ax\ge b$ we can divide both LHS and RHS by a keep the sign unchanged if a is a positive number. If a is a negative number then we can divide both LHS and RHS by a but we have reversed the sign if the sign is greater than equal to we have changed it to less than equal to. We can apply this to solve the given question.

Complete step by step answer:
The given inequality is $3x\ge 15$
We know that we can write the inequality $ax\ge b$ as $x\ge \dfrac{b}{a}$ when a is a positive number. The number a can not be negative or zero, for negative a we have reverse the sign and for 0 the inequality will be invalid because 0 can not be in denominator
So we can write the inequality $3x\ge 15$ as $x\ge \dfrac{15}{3}$ further solving we get $x\ge 5$
Range of x is form 5 to infinity
So we can write $x\in \left[ 5,\infty \right)$

Note:
Keep in mind that when solving an inequality, while multiplying or dividing any negative number in both LHS and RHS do not forget to reverse the comparison operator. Comparison operators include $>$ , $<$ , $\ge$ and $\le$ , other the whole solution will be wrong. For example if an inequality given as $-2x\le 40$ the final result of the inequality will be $x\ge -20$ after dividing both LHS and RHS by -2 we reverse sign $\le$ to $\ge$ so we can write $x\in \left[ -20,\infty \right)$ . We can check our answer by putting a random value of x form the answer in the inequality.