What is ((x+3))/3+((x+2))/5 >= ((7x-1))/(15) ?

The solution to ((x+3))/3+((x+2))/5 >= ((7x-1))/(15) is x>=-22

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((x+3))/3+((x+2))/5 >= ((7x-1))/(15)

\frac{( x + 3 )}{3} + \frac{( x + 2 )}{5} \geq \frac{( 7 x - 1 )}{15}

x \geq - 22

Interval Notation

[- 22, \infty)

Solution steps

\frac{( x + 3 )}{3} + \frac{( x + 2 )}{5} \geq \frac{( 7 x - 1 )}{15}

\frac{x + 3}{3} + \frac{x + 2}{5} \geq \frac{( 7 x - 1 )}{15}

Multiply by LCM

5 (x + 3) + 3 (x + 2) \geq 7 x - 1

Expand

5 (x + 3) + 3 (x + 2) : 8 x + 21

8 x + 21 \geq 7 x - 1

Move

21

to the right side

8 x \geq 7 x - 22

Move

7 x

to the left side

x \geq - 22

x - 2 < 0

\frac{( 2 x - 1 )}{5} - \frac{( 3 x + 1 )}{3} > \frac{( x - 5 )}{10}

20 x + 8 > 12 x + 16

x + 4 < 8

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

What is ((x+3))/3+((x+2))/5 >= ((7x-1))/(15) ?
The solution to ((x+3))/3+((x+2))/5 >= ((7x-1))/(15) is x>=-22