Question

Solve 5x-3>7; when
(a). x is an integer
(b). x is a real number

Answer 1

- Hint: Your first step should be to solve the inequality and get the inequality for the value of x and represent it in standard form. Now apply the condition for each subpart separately and get the values of x for each subpart accordingly.

Complete step-by-step solution -

Let us start the solution to the above question by solving the inequality to get all the possible values of x.
\[5x-3>7\]
Now if we take 3 to the other side of the inequality, we get
\[5x>7+3\]
\[5x>10\]
Now we will be taking the 5 from one side of the inequality to the other side to get the values of x. On doing so, we get
\[x>2\]
So, looking at the result, we can conclude that the values of x can be any real number greater than 2. So, the values that x can take if it is an integer includes all natural numbers except 1 and 2.
While if x is a real number then it can be any real number greater than 2.

Note: While handling an inequality, we should always be careful as whenever you multiply or divide an inequality by a negative number, the sign of inequality gets reversed. Also, be careful about the sign of inequality and the conditions given in the question.