Chapter 5, Problem 28SGR

To determine

To write an inequality for the given situation and to solve it.

Answer to Problem 28SGR

The number must be less than 1.

Explanation of Solution

Given:

Four times a number decreased by 6 is less than $-2$ .

Calculation:

Let $x$ be the required number, then four times of it is $4x$ .

Now when it is decreased by 6, we get $4x-6$ .

Therefore required inequality is,

  $4x-6<-2$

Adding 6 on both sides, we get

  $\begin{array}{l}\Rightarrow 4x-6+6<-2+6\\ \Rightarrow 4x<4\end{array}$

Dividing by 4 on both sides, we get

  $\begin{array}{l}\Rightarrow \frac{4x}{4}<\frac{4}{4}\\ \Rightarrow x<1\end{array}$

Hence the number must be less than 1.