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

The solution to (5x-2)/5 <(2-7x)/(-3) is x< 1/5

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(5x-2)/5 <(2-7x)/(-3)

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

x < \frac{1}{5}

Interval Notation

(- \infty, \frac{1}{5})

Decimal Notation

x < 0.2

Solution steps

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

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

(5 x - 2) (- 3) < 5 (2 - 7 x)

Simplify

- 3 (5 x - 2) < 5 (2 - 7 x)

Expand

- 3 (5 x - 2) : - 15 x + 6

Expand

5 (2 - 7 x) : 10 - 35 x

- 15 x + 6 < 10 - 35 x

Move

6

to the right side

- 15 x < - 35 x + 4

Move

35 x

to the left side

20 x < 4

Divide both sides by

20

x < \frac{1}{5}

b^{2} - 9 b + 14

25 6^{- \frac{1}{4}}

3^{6}

\frac{2}{3} \cdot \frac{5}{9}

2 (x + 2 x) = 36