Question

How do I solve rational inequality $\dfrac{{x + 2}}{{2x + 1}} > 5$using a T1-84?

Answer 1

Hint:
In this question we are asked to solve the inequality using T1-84 calculator which is a graphing calculator, to solve the inequality we need to graph the given equations in the T1-84 calculator, step by step.

Complete step by step solution:
The TI-84 Plus graphing calculator is ideal for high school math and science. Its MathPrint feature engages students by enabling them to enter fractions and equations in proper notation so they see it on the display exactly as it's printed in text and on the board.
Given inequality is $\dfrac{{x + 2}}{{2x + 1}} > 5$,
Now we need to solve the inequality using T1-84 calculator,
We know that T1-84 is a graphing calculator that displays 16-digits .
To solve the inequality,
First we need to enter the left hand side of the equation into Y1 which is, $\dfrac{{x + 2}}{{2x + 1}}$,
Then enter the right hand side of the equation into Y2, which us 4,
Then press INTERCEPT option, and use parenthesis for the denominators in this question.
Now the required result is shown on the screen of the T1-84 calculator, which will be \[x \in \left( { - \infty ,\dfrac{{ - 1}}{3}} \right)\].
And the graph showing the area under the intervals will be displayed on the screen of the T1-84 calculator.

Note:
We can also solve the inequality algebraically, which is given by,
Given $\dfrac{{x + 2}}{{2x + 1}} > 5$,
Now take denominator to the right hand side,
$ \Rightarrow x + 2 > 5\left( {2x + 1} \right)$,
Now multiplying we get,
$ \Rightarrow x + 2 > 10x + 5$,
Now taking all $x$ terms to one side and constants to one side we get,
$ \Rightarrow 2 - 5 > 10x - x$,
Now simplifying we get,
$ \Rightarrow - 3 > 9x$,
Now dividing both sides with 9 we get,
$ \Rightarrow $ $ \Rightarrow \dfrac{{ - 3}}{9} > \dfrac{{9x}}{9}$,
Now simplifying we get,
$ \Rightarrow \dfrac{{ - 1}}{3} > x$,
Now rewriting the equation we get,
$ \Rightarrow x < \dfrac{{ - 1}}{3}$,
So, the solution will be \[x \in \left( { - \infty ,\dfrac{{ - 1}}{3}} \right)\].