Question

Solve: $3x-7>5x-1$ when x is an integer.

Answer 1

Hint: We will first start by arranging the terms in an order such that all the terms with x are one side and the rest terms on another side. Then we will use the principle of inequality to find the range of value of x.

Complete step-by-step answer:
Now, we have been given that $3x-7>5x-1$.
Now, we will move 5x from RHS to LHS by subtracting 5x from both sides and -7 from LHS to RHS by adding +7 on both sides. So, we have,
$$3x-5x-7+7>5x-1-5x+7-2x>6$$
Now, we know that on multiplying both sides by -1. We have the sign of inequality reversed. So, we have,
$2x<-6$
Now, dividing both sides by 2 we have,
$$\begin{array}{rl}& x<{\displaystyle \frac{-6}{2}}\\ & x<-3\end{array}$$
Which can be shown on number line as,

Note: It is important to note that we have changed the sign of inequality on multiplying the both sides by -1. For example, we know that -2 < 3. Now, if we multiply by -1 on both sides with signs of inequality changing. We have +2 < -3 which is not true. Hence, the sign of inequality is changed on multiplying or dividing an inequality by a negative number.