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

The solution to ((2(x-2)))/5 >((x+2))/2 is x<-18

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

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

x < - 18

Interval Notation

(- \infty, - 18)

Solution steps

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

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

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

Simplify

4 (x - 2) > 5 (x + 2)

Expand

4 (x - 2) : 4 x - 8

Expand

5 (x + 2) : 5 x + 10

4 x - 8 > 5 x + 10

Move

8

to the right side

4 x > 5 x + 18

Move

5 x

to the left side

- x > 18

Multiply both sides by

- 1

x < - 18

3 x + 8 > 7 (x - 2)

2 i < 6 u

- 5 + 3 (2 x + 1) > 3 (- 2 - x) + 10

3 x \geq 5 x + 8

2 x - 5 < - 3

What is ((2(x-2)))/5 >((x+2))/2 ?
The solution to ((2(x-2)))/5 >((x+2))/2 is x<-18