Chapter 12, Problem 59CUR

To determine

To solve : The inequality, graph and check the solution.

Answer to Problem 59CUR

The solution is $x>6$ . i.e. all the numbers greater than $6$ is the solution.

Explanation of Solution

Given information : $\frac{4}{9}x-2>\frac{2}{3}$

Formula used : Adding or subtracting the same number on each side of an inequality produces an equivalent inequality.

Multiplying each side of an inequality by a positive number produces an equivalent inequality.

Multiplying each side of an inequality by a negative numbers and reversing the direction of the inequality symbol produces an equivalent inequality.

Dividing each side of an inequality by a positive number produces an equivalent inequality.

Dividing each side of an inequality by a negative numbers and reversing the direction of the inequality symbol produces an equivalent inequality.

Calculation :

  $\begin{array}{l}\frac{4}{9}x-2>\frac{2}{3}\\ 9\times \left(\frac{4}{9}x-2\right)>9\times \frac{2}{3}\\ 9\times \frac{4}{9}x-9\times 2>3\times 2\\ 4x-18>6\\ 4x-18+18>6+18\\ 4x>24\\ \frac{4x}{4}>\frac{24}{4}\\ x>6\end{array}$

Check:

$9$ is the number greater than $6$ . Putting $10$ on the place of $x$ in the left hand side of the given inequality we get,

  $\begin{array}{c}\frac{4}{9}x-2=\frac{4}{9}\times \left(9\right)-2\\ =4-2\\ =2\end{array}$

  $2>\frac{2}{3}$

Therefore, the solution is right.

Graph :

The solution is $x>6$ .

Interpretation : The solution is $x>6$ . i.e. all the numbers greater than $6$ is the solution.