Q43. - Algebra 2

Question

We have to find the point which satisfy the inequality$y>5\left|x\right|-3$

The options are

$\begin{array}{l}A.(2,2)\\ B.(-1,3)\\ C.(3,7)\\ D.(-2,4)\end{array}$

Step-by-Step Solution

Answer

The option B is correct and right.

Step-1 – Write the given inequality

Here the inequality is given as $y>5\left|x\right|-3$

We have to put the value or point in the inequality to find which inequality is correct.

Step-2 – Put each value to find whether the inequality is true or not.

By putting the value from the option as

Here first option is $\left(2,2\right)$ in the inequality $y>5\left|x\right|-3$as

$\begin{array}{l}y>5\left|x\right|-3\\ 2>5\left|2\right|-3\\ 2>7\end{array}$

Which is not true.

Here by putting the second option $\left(-1,3\right)$ in the inequality $y>5\left|x\right|-3$ as

$\begin{array}{l}y>5\left|x\right|-3\\ 3>5\left|-1\right|-3\\ 3>5-3\\ 3>2\end{array}$

Which is true.

Now by putting the third option $\left(3,7\right)$in the inequality as

$\begin{array}{l}y>5\left|x\right|-3\\ 7>5\left|3\right|-3\\ 7>15-3\\ 7>12\end{array}$

Which is not true.

Now by putting the fourth option $\left(-2,4\right)$in the inequality as

$\begin{array}{l}y>5\left|x\right|-3\\ 4>5\left|-2\right|-3\\ 4>10-3\\ 4>7\end{array}$

Which is not true.

Therefore, the option B is correct and right.