Question

How do you solve \[5x\ge 30\] ?

Answer 1

Hint: In the above question we are provided with the inequality of the form \[ax\ge b\]. So, to solve it we will follow a few steps. First, we will know whether the given equation is in simplified form. After that we will simplify further by combining like terms and then perform simple addition or subtraction to get a variable on one side and the constant on the other side. Solve the simplified inequality to get the answer.

Complete step by step answer:
Now before coming to the question let us get familiar with inequalities and rules to be followed while solving it.
Inequalities are the mathematical relations which we use to make a non-equal comparison between two expressions. To solve an inequality, we have to follow some rules. If you add, subtract, divide or multiply any number on both sides, the inequality remains the same. If we multiply both sides by the same negative number then we have to reverse the sign of equality. If we divide both sides by the same negative number in this case also, we have to reverse the sign of equality.
Now coming to the question, we have \[5x\ge 30\] .
Here we can see that the inequality is already in simplified form.
Therefore we will perform basic operations to get the value of x .
\[\begin{align}
  & 5x\ge 30 \\
 & \Rightarrow x\ge \dfrac{30}{5} \\
 & \Rightarrow x\ge 6 \\
\end{align}\]
We can conclude that \[x\in [6,\infty )\] .
Thus, \[x\ge 6\] is the required answer.

Note: Remember the approach used above to solve the question for future use. Since, whenever you are dealing with inequalities, keep in mind the rules to solve the inequality and by which operation you have to reverse the sign of the inequality. Do not get confused by signs while finding the range of the variable.