What is (-2x+5)/3 >(3(2x+7))/5 ?

The solution to (-2x+5)/3 >(3(2x+7))/5 is x<-19/14

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(-2x+5)/3 >(3(2x+7))/5

\frac{- 2 x + 5}{3} > \frac{3 ( 2 x + 7 )}{5}

x < - \frac{19}{14}

Interval Notation

(- \infty, - \frac{19}{14})

Decimal Notation

x < - 1.35714 \dots

Solution steps

\frac{- 2 x + 5}{3} > \frac{3 ( 2 x + 7 )}{5}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

(- 2 x + 5) \cdot 5 > 3 \cdot 3 (2 x + 7)

Simplify

(- 2 x + 5) \cdot 5 > 9 (2 x + 7)

Expand

(- 2 x + 5) \cdot 5 : - 10 x + 25

Expand

9 (2 x + 7) : 18 x + 63

- 10 x + 25 > 18 x + 63

Move

25

to the right side

- 10 x > 18 x + 38

Move

18 x

to the left side

- 28 x > 38

Multiply both sides by

- 1

28 x < - 38

Divide both sides by

28

x < - \frac{19}{14}

4 x + 1 > 3

\frac{x}{2} > 5

12 > x + 8

2 x - 3 > 0

3 x - 2 > 2 x - 2

What is (-2x+5)/3 >(3(2x+7))/5 ?
The solution to (-2x+5)/3 >(3(2x+7))/5 is x<-19/14