Chapter 1.9, Problem 27E

Solution

To calculate: The value of x for the inequality $x^2+2x-3>0$ using a table.

The solution of the inequality is $x<-3\text{and}x>1$ .

Given information:

The inequality is $x^2+2x-3>0$ .

Formula used:

Substitute the values for x into the inequality.

Calculation:

Write the given inequality:

  $x^2+2x-3>0$

Substitute the $x=-4$ in the inequality,

  $\begin{array}{c}{\left(-4\right)}^2+2\left(-4\right)-3>0\\ 16-8-3>0\\ 5>0\end{array}$

Substitute the $x=-3$ in the inequality,

  $\begin{array}{c}{\left(-3\right)}^2+2\left(-3\right)-3>0\\ 9-6-3>0\\ 0=0\end{array}$

Substitute the $x=-2$ in the inequality,

  $\begin{array}{c}{\left(-2\right)}^2+2\left(-2\right)-3>0\\ 4-4-3>0\\ -3<0\end{array}$

Similarly make a table by substituting the values of x in the inequality:

x	$-5$	$-4$	$-3$	$-2$	$-1$	0	1	2	3
$x^2+2x-3$	12	5	0	$-3$	$-4$	$-3$	0	5	12

It can be seen that $x^2+2x-3>0$ if values of x are taken less than $-3$ and more than 1 are substituted in the inequality.

Therefore, $x<-3\text{and}x>1$ are the solutions for the inequality $x^2+2x-3>0$ .