Question

How do you solve \[4+\dfrac{n}{3}<6\] ?

Answer 1

Hint: A mathematical expressions contain such symbols ‘<’ (less than symbol), ‘>’ (more than symbol), \['\le '\] (less than or equal to symbol), \['\ge '\] (more than or equal to symbol), they are known as inequalities. To solve the given question, you need to solve the given inequality by adding, subtracting, multiplication or dividing both sides until you are left with the variable on its own.

Complete step by step solution:
We have the given inequality:
\[4+\dfrac{n}{3}<6\]
Subtracting 4 from both the sides of the given inequality, we get
\[4+\dfrac{n}{3}-4<6-4\]
\[\dfrac{n}{3}<2\]
Multiply both the sides of the given inequality by 3, we get
\[\dfrac{n}{3}\times 3<2\times 3\]
Simplify the inequality further, we obtain
\[n<6\]
Therefore, all the real numbers that are less than 6, are the solutions of the given inequality.Hence, the solution set is \[\left( -\infty ,6 \right)\].

Additional information:
Solve in this way also:
We have the given expression:
\[4+\dfrac{n}{3}<6\]
Multiply the given inequality by 3,
\[12+n<18\]
Subtract 12 from both the sides,
\[12+n-12<18-12\]
Therefore, \[n<6\]

Note: You can solve the simple inequality just by doing basic mathematical operations such as addition, subtraction, multiplication and division. You can apply these mathematical operations to both the sides of the given inequality until you are left with the variable on its own.
-But in some cases that result into the change of direction of the inequality:
-When we multiply or divide both the sides by a negative number.
-When we swap the right hand sides and the left hand sides.
Linear inequality has only one solution set that contains any number of solutions. Every solution must satisfy the inequality.