What is ((x-3))/(2x+1)<4 ?

The solution to ((x-3))/(2x+1) -1/2

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((x-3))/(2x+1)<4

\frac{( x - 3 )}{2 x + 1} < 4

x < - 1 or x > - \frac{1}{2}

Solution steps

\frac{x - 3}{2 x + 1} < 4

Rewrite in standard form

\frac{- 7 x - 7}{2 x + 1} < 0

Factor

\frac{- 7 x - 7}{2 x + 1} : \frac{- 7 ( x + 1 )}{2 x + 1}

\frac{- 7 ( x + 1 )}{2 x + 1} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 7 ( x + 1 ) ) ( - 1 )}{2 x + 1} > 0 \cdot (- 1)

Simplify

\frac{7 ( x + 1 )}{2 x + 1} > 0

Divide both sides by

7

\frac{\frac{7 ( x + 1 )}{2 x + 1}}{7} > \frac{0}{7}

Simplify

\frac{x + 1}{2 x + 1} > 0

Identify the intervals

x < - 1 or x > - \frac{1}{2}

\frac{2}{7} - \frac{5}{21} \frac{1}{7}

(\frac{7}{12})^{2}

- 6 x^{2} + 48 x - 72

4 a^{2} - 4 a + 1