MHB Solve the inequality and graph the solution on a real number line

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To solve the inequality (3x - 5)/(x - 5) > 4, first subtract 4 from both sides to obtain (3x - 5)/(x - 5) - 4 > 0. Next, combine the terms on the left side to create a single fraction. Identify critical points where the numerator and denominator equal zero, as these will help determine the intervals for testing the inequality. Finally, graph the solution on a real number line, marking the critical points and indicating where the inequality holds true.
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(3x - 5)/(x - 5) > 4

How does one complete this problem?
 
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We are given to solve:

$$\frac{3x-5}{x-5}>4$$

Now, one might be tempted to multiply through by $x-5$ to clear the denominator on the right side, as we would with an equation. But with inequalities, we have to be mindful of the sign of a multiplicative quantity, so our best strategy here is to subtract 4 from both sides:

$$\frac{3x-5}{x-5}-4>0$$

Now, you need to combine terms on the left, and then determine your critical numbers, which are found anywhere the numerator AND denominator is zero. Can you proceed?
 
Yes, thank you.
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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