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

The solution to (3-1/3 x)/(3+1/2)>= (3x-5/2)/(1-2/3) is x<= 351/382

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

\frac{3 - \frac{1}{3} x}{3 + \frac{1}{2}} \geq \frac{3 x - \frac{5}{2}}{1 - \frac{2}{3}}

x \leq \frac{351}{382}

Interval Notation

(- \infty, \frac{351}{382}]

Decimal Notation

x \leq 0.91884 \dots

Solution steps

\frac{3 - \frac{1}{3} x}{3 + \frac{1}{2}} \geq \frac{3 x - \frac{5}{2}}{1 - \frac{2}{3}}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

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

Simplify

1 - \frac{1}{9} x \geq \frac{7}{2} (3 x - \frac{5}{2})

Expand

\frac{7}{2} (3 x - \frac{5}{2}) : \frac{21}{2} x - \frac{35}{4}

1 - \frac{1}{9} x \geq \frac{21}{2} x - \frac{35}{4}

Move

1

to the right side

- \frac{1}{9} x \geq - \frac{39}{4} + \frac{21}{2} x

Move

\frac{21}{2} x

to the left side

- \frac{191}{18} x \geq - \frac{39}{4}

Multiply both sides by

- 1

\frac{191}{18} x \leq \frac{39}{4}

Multiply both sides by

18

191 x \leq \frac{351}{2}

Divide both sides by

191

x \leq \frac{351}{382}

- 2 (5 + 6 c) + 16 = - 90

(2 u^{2} v^{3})^{3} (3 u^{- 3} v)^{2}

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

- 25 a^{2} + 185 a - 70

\frac{1}{4} x - \frac{1}{5} x + \frac{1}{20} x = 4

What is (3-1/3 x)/(3+1/2)>= (3x-5/2)/(1-2/3) ?
The solution to (3-1/3 x)/(3+1/2)>= (3x-5/2)/(1-2/3) is x<= 351/382