Chapter 12, Problem 45CUR

To determine

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

Answer to Problem 45CUR

The solution is $x>-7$ . i.e. all the numbers greater than $\left(-7\right)$ is the solution.

Explanation of Solution

Given information : $4+3x>-17$

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

  $\begin{array}{l}4+3x>-17\\ 4+3x-4>-17-4\\ 3x>-21\\ \frac{3x}{3}>\frac{-21}{3}\\ x>-7\end{array}$

Check:

$10$ is the number greater than $-7$ . Putting $10$ on the place of $x$ in the left hand side of the given inequality we get,

  $\begin{array}{c}4+3x=7+\left(3\times 10\right)\\ =7+30\\ =37\end{array}$

  $37>-17$

Therefore, the solution is right.

Graph :

The solution is $x>-7$ .

Interpretation : The solution is $x>-7$ . i.e. all the numbers greater than $\left(-7\right)$ is the solution.