Chapter 5.3, Problem 24PPS

To determine

To solve the inequality:

  $\frac{7}{10}x+14<49$

And check the solution.

Answer to Problem 24PPS

  $x<50$

Explanation of Solution

Given:

  $\frac{7}{10}x+14<49$

Concept Used:

• To check the answer solution for the given inequality

1. First check the solution at end point by converting it into an equation.
2. If the solution is $x<m$, then pick any value of x less than m and check whether it satisfies the inequality.
3. If the solution is $x>m$, then pick any value of x greater than m and check whether it satisfies the inequality.

Properties of inequality:

1. $b\le c\Rightarrow ab\le ac,\text{ if }a\ge 0$
2. $b\le c\Rightarrow ab\ge ac,\text{ if }a\le 0$

Calculation:

Let the number be x, seven tenth of a number x is added to 14 can be written as:

  $\frac{7}{10}x+14$

Now, then (7/10) x + 14 value is less than forty nine is written as:

  $\begin{array}{l}\frac{7}{10}x+14<49\\ \Rightarrow \frac{7}{10}x+14-14<49-14\\ \Rightarrow \frac{7}{10}x<35\end{array}$

Multiply each side by 10/7 to solve the value of x:

  $\begin{array}{c}\frac{7}{10}x<35\\ \frac{10}{7}\cdot \frac{7}{10}x<\frac{10}{7}\cdot 35\\ x<50\end{array}$

Thus, the inequality is true for x is greater than 50, thus the solution of given inequality in interval form is:

  $\left(-\infty ,50\right)$

Put any value any value of x less than 50, say 40 and check whether it satisfies the inequality, as

  $\begin{array}{c}x=40:\frac{7}{10}\left(x\right)+14<49\\ \frac{7}{10}\left(40\right)+14<49\\ 28+14<49\\ 42<49\end{array}$

Since, the condition satisfied thus solution of inequality is correct.