Chapter A, Problem 42E

To determine

To solve the below inequality in terms of intervals where a, b and care negative constants-

  $ax+b<c$

Answer to Problem 42E

The solution of the inequality is $x>\frac{c-b}{a}$

Explanation of Solution

Given: Inequality: $ax+b<c$

Formula Used:

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.

Real number line is the line whose points are the real numbers. 

Calculation:

Given : Inequality equation is $ax+b<c$

Subtracting $b$ from both the sides, we have:

  $\begin{array}{l}ax+b-b<c-b\\ ax<c-b\end{array}$

Divide both the sides by $a$ and reversing the sign since $a$ is negative constant, we have:

  $\begin{array}{l}\frac{ax}{a}>\frac{c-b}{a}\\ x>\frac{c-b}{a}\end{array}$

Conclusion:

Hence, the solution of the inequality is $x>\frac{c-b}{a}$