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

The solution to x/2 >= ((5x-2))/3-((7x-3))/5 is x>=-2/7

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

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

x \geq - \frac{2}{7}

Interval Notation

[- \frac{2}{7}, \infty)

Decimal Notation

x \geq - 0.28571 \dots

Solution steps

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

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

Multiply by LCM

15 x \geq 10 (5 x - 2) - 6 (7 x - 3)

Expand

10 (5 x - 2) - 6 (7 x - 3) : 8 x - 2

15 x \geq 8 x - 2

Move

8 x

to the left side

7 x \geq - 2

Divide both sides by

7

x \geq - \frac{2}{7}

6 (3 x - 1) - 5 (4 x - 3) \geq 9 - 2 x

x < \frac{- 3}{2}

4 - 3 (x - 2) < 3 + 2 (x + 6)

8 + 4 x > 6

\frac{( 5 x - 2 )}{3} - \frac{( x - 8 )}{4} \geq \frac{( x + 14 )}{2}

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