What is (2x-7)/7 >= (9x-2)/3 ?

The solution to (2x-7)/7 >= (9x-2)/3 is x<=-7/57

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(2x-7)/7 >= (9x-2)/3

\frac{2 x - 7}{7} \geq \frac{9 x - 2}{3}

x \leq - \frac{7}{57}

Interval Notation

(- \infty, - \frac{7}{57}]

Decimal Notation

x \leq - 0.12280 \dots

Solution steps

\frac{2 x - 7}{7} \geq \frac{9 x - 2}{3}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

(2 x - 7) \cdot 3 \geq 7 (9 x - 2)

Expand

(2 x - 7) \cdot 3 : 6 x - 21

Expand

7 (9 x - 2) : 63 x - 14

6 x - 21 \geq 63 x - 14

Move

21

to the right side

6 x \geq 63 x + 7

Move

63 x

to the left side

- 57 x \geq 7

Multiply both sides by

- 1

57 x \leq - 7

Divide both sides by

57

x \leq - \frac{7}{57}

6 (y - 2) - 5 y = 4 (y + 3)

- 5 X (- 3 X - 1) > 2 (- X + 1)

30 < 2 x - 6

0.25 \cdot 6

\frac{3 c - 2}{8 c} - \frac{5 c - 2}{6 c}