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

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

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

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

x > - 1

Solution steps

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

Rewrite in standard form

\frac{- 2 x ^{2} - 2 x - 3}{2 x + 2} < 0

Factor

\frac{- 2 x ^{2} - 2 x - 3}{2 x + 2} : \frac{- 2 x ^{2} - 2 x - 3}{2 ( x + 1 )}

\frac{- ( 2 x ^{2} + 2 x + 3 )}{2 ( x + 1 )} < 0

Simplify

\frac{- ( 2 x ^{2} + 2 x + 3 )}{2 ( x + 1 )} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( 2 x ^{2} + 2 x + 3 ) ) ( - 1 )}{2 ( x + 1 )} > 0 \cdot (- 1)

Simplify

\frac{2 x ^{2} + 2 x + 3}{2 ( x + 1 )} > 0

Multiply both sides by

2

\frac{2 ( 2 x ^{2} + 2 x + 3 )}{2 ( x + 1 )} > 0 \cdot 2

Simplify

\frac{2 x ^{2} + 2 x + 3}{x + 1} > 0

Identify the intervals

x > - 1

7 x + 2 x = 2 x + 1 + 6 x

z^{2} - 81

4 + \frac{1}{4}

e^{- 2}

m \cdot 5 = 10